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[Axiom-developer] 20071006.01.tpd.patch
|
From: |
daly |
|
Subject: |
[Axiom-developer] 20071006.01.tpd.patch |
|
Date: |
Sat, 6 Oct 2007 01:06:19 -0500 |
This patch adds Axiom regression tests of Kamke ODEs 301-350
========================================================================
diff --git a/changelog b/changelog
index 916c822..c63be68 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,5 @@
+20071005 tpd src/input/Makefile kamke6.input regression test added
+20071005 tpd src/input/kamke6.input ODE regression test added
20071005 tpd src/input/Makefile kamke5.input regression test added
20071005 tpd src/input/kamke5.input ODE regression test added
20071005 tpd src/input/Makefile kamke4.input regression test added
diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet
index 1d2626f..3d92581 100644
--- a/src/input/Makefile.pamphlet
+++ b/src/input/Makefile.pamphlet
@@ -323,7 +323,7 @@ REGRES= algaggr.regress algbrbf.regress algfacob.regress
alist.regress \
iprntpk.regress \
ipftest.regress is.regress isprime.regress kafile.regress \
kamke0.regress kamke1.regress kamke2.regress kamke3.regress \
- kamke4.regress kamke5.regress \
+ kamke4.regress kamke5.regress kamke6.regress \
kernel.regress knot2.regress kovacic.regress kuipers.regress \
laplace.regress leg.regress limit.regress lindep.regress \
list.regress lode.regress lodesys.regress lodo1.regress \
@@ -564,7 +564,7 @@ FILES= ${OUT}/algaggr.input ${OUT}/algbrbf.input
${OUT}/algfacob.input \
${OUT}/ipftest.input ${OUT}/is.input ${OUT}/isprime.input \
${OUT}/kafile.input ${OUT}/kamke0.input ${OUT}/kamke1.input \
${OUT}/kamke2.input ${OUT}/kamke3.input ${OUT}/kamke4.input \
- ${OUT}/kamke5.input \
+ ${OUT}/kamke5.input ${OUT}/kamke6.input \
${OUT}/kernel.input ${OUT}/knot.input \
${OUT}/kovacic.input ${OUT}/kuipers.input \
${OUT}/laplace.input ${OUT}/leg.input ${OUT}/lexp.input \
@@ -833,6 +833,7 @@ DOCFILES= \
${DOC}/kamke0.input.dvi ${DOC}/kamke1.input.dvi \
${DOC}/kamke2.input.dvi ${DOC}/kamke3.input.dvi \
${DOC}/kamke4.input.dvi ${DOC}/kamke5.input.dvi \
+ ${DOC}/kamke6.input.dvi \
${DOC}/kernel.input.dvi ${DOC}/knot2.input.dvi \
${DOC}/knot.input.dvi ${DOC}/knownbugs.input.dvi \
${DOC}/kovacic.input.dvi ${DOC}/kuipers.input.dvi \
diff --git a/src/input/kamke6.input.pamphlet b/src/input/kamke6.input.pamphlet
new file mode 100644
index 0000000..ad31cd3
--- /dev/null
+++ b/src/input/kamke6.input.pamphlet
@@ -0,0 +1,3661 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/src/input kamke6.input}
+\author{Timothy Daly}
+\maketitle
+\begin{abstract}
+This is the 301-350 of the Kamke test suite as published by
+E. S. Cheb-Terrab\cite{1}. They have been rewritten using Axiom
+syntax. Where possible we show that the particular solution actually
+satisfies the original ordinary differential equation.
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+<<*>>=
+)spool kamke6.output
+)set break resume
+)set mes auto off
+)clear all
+
+--S 1 of 120
+y:=operator 'y
+--R
+--R
+--R (1) y
+--R Type:
BasicOperator
+--E 1
+
+--S 2 of 120
+--Rf:=operator 'f
+--R
+--R
+--R (2) f
+--R Type:
BasicOperator
+--E 2
+
+--S 3 of 120
+--Rg:=operator 'g
+--R
+--R
+--R (3) g
+--R Type:
BasicOperator
+--R
+--E 3
+
+--S 4 of 120
+--Rode301 := (6*x*y(x)**2+x**2)*D(y(x),x)-y(x)*(3*y(x)**2-x)
+--R
+--R
+--R 2 2 , 3
+--R (4) (6x y(x) + x )y (x) - 3y(x) + x y(x)
+--R
+--R Type: Expression
Integer
+--E 4
+
+--S 5 of 120
+--Rsolve(ode301,y,x)
+--R
+--R
+--R (5) "failed"
+--R Type:
Union("failed",...)
+--E 5
+
+--S 6 of 120
+--Rode302 := (x**2*y(x)**2+x)*D(y(x),x)+y(x)
+--R
+--R
+--R 2 2 ,
+--R (6) (x y(x) + x)y (x) + y(x)
+--R
+--R Type: Expression
Integer
+--E 6
+
+--S 7 of 120
+--Rsolve(ode302,y,x)
+--R
+--R
+--R (7) "failed"
+--R Type:
Union("failed",...)
+--E 7
+
+--S 8 of 120
+--Rode303 := (x*y(x)-1)**2*x*D(y(x),x)+(x**2*y(x)**2+1)*y(x)
+--R
+--R
+--R 3 2 2 , 2 3
+--R (8) (x y(x) - 2x y(x) + x)y (x) + x y(x) + y(x)
+--R
+--R Type: Expression
Integer
+--E 8
+
+--S 9 of 120
+--Rsolve(ode303,y,x)
+--R
+--R
+--R (9) "failed"
+--R Type:
Union("failed",...)
+--E 9
+
+--S 10 of 120
+--Rode304 := (10*x**3*y(x)**2+x**2*y(x)+2*x)*D(y(x),x)+5*x**2*y(x)**3+x*y(x)**2
+--R
+--R
+--R 3 2 2 , 2 3 2
+--R (10) (10x y(x) + x y(x) + 2x)y (x) + 5x y(x) + x y(x)
+--R
+--R Type: Expression
Integer
+--E 10
+
+--S 11 of 120
+--Rsolve(ode304,y,x)
+--R
+--R
+--R (11) "failed"
+--R Type:
Union("failed",...)
+--E 11
+
+--S 12 of 120
+--Rode305 := (y(x)**3-3*x)*D(y(x),x)-3*y(x)+x**2
+--R
+--R
+--R 3 , 2
+--R (12) (y(x) - 3x)y (x) - 3y(x) + x
+--R
+--R Type: Expression
Integer
+--E 12
+
+--S 13 of 120
+--Ryx:=solve(ode305,y,x)
+--R
+--R
+--R 4 3
+--R 3y(x) - 36x y(x) + 4x
+--R (13) -----------------------
+--R 12
+--R Type: Union(Expression
Integer,...)
+--E 13
+
+--S 14 of 120
+--Rode305expr := (yx**3-3*x)*D(yx,x)-3*yx+x**2
+--R
+--R
+--R (14)
+--R 15 12 3 11 2 9 4
8
+--R 27y(x) - 1053x y(x) + 108x y(x) + 14580x y(x) - 2916x y(x)
+--R +
+--R 6 7 3 6 5 5 7 4
+--R 144x y(x) - 81648x y(x) + 23328x y(x) - 2160x y(x)
+--R +
+--R 9 4 3 6 2 8
10
+--R (64x + 139968x - 5184x)y(x) - 46656x y(x) + 5184x y(x) - 192x
+--R +
+--R 2
+--R 15552x
+--R *
+--R ,
+--R y (x)
+--R
+--R +
+--R 13 2 12 10 3 9 5 8
+--R - 81y(x) + 27x y(x) + 2916x y(x) - 1296x y(x) + 108x y(x)
+--R +
+--R 2 7 4 6 6 5
+--R - 34992x y(x) + 19440x y(x) - 3024x y(x)
+--R +
+--R 8 3 4 5 3 7 2
+--R (144x + 139968x - 1296)y(x) - 93312x y(x) + 20736x y(x)
+--R +
+--R 9 11 3 2
+--R (- 1920x + 31104x)y(x) + 64x - 6912x + 1728x
+--R /
+--R 1728
+--R Type: Expression
Integer
+--E 14
+
+--S 15 of 120
+--Rode306 := (y(x)**3-x**3)*D(y(x),x)-x**2*y(x)
+--R
+--R
+--R 3 3 , 2
+--R (15) (y(x) - x )y (x) - x y(x)
+--R
+--R Type: Expression
Integer
+--E 15
+
+--S 16 of 120
+--Ryx:=solve(ode306,y,x)
+--R
+--R
+--R 6 3 3
+--R y(x) - 2x y(x)
+--R (16) ----------------
+--R 6
+--R Type: Union(Expression
Integer,...)
+--E 16
+
+--S 17 of 120
+--Rode306expr := (yx**3-x**3)*D(yx,x)-x**2*yx
+--R
+--R
+--R (17)
+--R 23 3 20 6 17 9 14 12 11
+--R y(x) - 7x y(x) + 18x y(x) - 20x y(x) + 8x y(x)
+--R +
+--R 3 5 6 2
+--R - 216x y(x) + 216x y(x)
+--R *
+--R ,
+--R y (x)
+--R
+--R +
+--R 2 21 5 18 8 15 11 12 2 6 5
3
+--R - x y(x) + 6x y(x) - 12x y(x) + 8x y(x) - 36x y(x) + 288x
y(x)
+--R /
+--R 216
+--R Type: Expression
Integer
+--E 17
+
+--S 18 of 120
+--Rode307 := (y(x)**2+x**2+a)*y(x)*D(y(x),x)+(y(x)**2+x**2-a)*x
+--R
+--R
+--R 3 2 , 2 3
+--R (18) (y(x) + (x + a)y(x))y (x) + x y(x) + x - a x
+--R
+--R Type: Expression
Integer
+--E 18
+
+--S 19 of 120
+--Ryx:=solve(ode307,y,x)
+--R
+--R
+--R 4 2 2 4 2
+--R y(x) + (2x + 2a)y(x) + x - 2a x
+--R (19) ------------------------------------
+--R 4
+--R Type: Union(Expression
Integer,...)
+--E 19
+
+--S 20 of 120
+--Rode307expr := (yx**2+x**2+a)*yx*D(yx,x)+(yx**2+x**2-a)*x
+--R
+--R
+--R (20)
+--R 15 2 13 4 2 2 11
+--R y(x) + (7x + 7a)y(x) + (21x + 30a x + 18a )y(x)
+--R +
+--R 6 4 2 2 3 9
+--R (35x + 45a x + 30a x + 20a )y(x)
+--R +
+--R 8 6 2 4 3 2 4 7
+--R (35x + 20a x - 12a x + (- 16a + 16)x + 8a + 16a)y(x)
+--R +
+--R 10 8 2 6 3 4 4
2
+--R 21x - 15a x - 36a x + (- 24a + 48)x + (- 24a + 96a)x
+--R +
+--R 2
+--R 48a
+--R *
+--R 5
+--R y(x)
+--R +
+--R 12 10 2 8 3 6 4 4
2 2
+--R 7x - 18a x - 6a x + (16a + 48)x + (24a + 80a)x +
64a x
+--R +
+--R 3
+--R 32a
+--R *
+--R 3
+--R y(x)
+--R +
+--R 14 12 2 10 3 8 4 6 2 4 3 2
+--R (x - 5a x + 6a x + (4a + 16)x - 8a x - 48a x - 32a x
)y(x)
+--R *
+--R ,
+--R y (x)
+--R
+--R +
+--R 14 3 12 5 3 2 10
+--R x y(x) + (7x + 5a x)y(x) + (21x + 18a x + 6a x)y(x)
+--R +
+--R 7 5 2 3 3 8
+--R (35x + 15a x - 6a x + (- 4a + 4)x)y(x)
+--R +
+--R 9 7 2 5 3 3 4 6
+--R (35x - 20a x - 36a x + (- 16a + 32)x + (- 8a + 32a)x)y(x)
+--R +
+--R 11 9 2 7 3 5 4 3 2
4
+--R (21x - 45a x - 12a x + (24a + 72)x + (24a + 80a)x + 32a
x)y(x)
+--R +
+--R 13 11 2 9 3 7 4 5 2 3 3
2
+--R (7x - 30a x + 30a x + (16a + 64)x - 24a x - 96a x - 32a
x)y(x)
+--R +
+--R 15 13 2 11 3 9 4 7 3
3
+--R x - 7a x + 18a x + (- 20a + 20)x + (8a - 48a)x + (32a +
64)x
+--R +
+--R - 64a x
+--R /
+--R 64
+--R Type: Expression
Integer
+--E 20
+
+--S 21 of 120
+--Rode308 := 2*y(x)**3*D(y(x),x)+x*y(x)**2
+--R
+--R
+--R 3 , 2
+--R (21) 2y(x) y (x) + x y(x)
+--R
+--R Type: Expression
Integer
+--E 21
+
+--S 22 of 120
+--Ryx:=solve(ode308,y,x)
+--R
+--R
+--R 2 2
+--R 2y(x) + x
+--R (22) -----------
+--R 2
+--R Type: Union(Expression
Integer,...)
+--E 22
+
+--S 23 of 120
+--Rode308expr := 2*yx**3*D(yx,x)+x*yx**2
+--R
+--R
+--R (23)
+--R 7 2 5 4 3 6 , 6
+--R (16y(x) + 24x y(x) + 12x y(x) + 2x y(x))y (x) + 8x y(x)
+--R
+--R +
+--R 3 4 5 3 2 7 5
+--R (12x + 4x)y(x) + (6x + 4x )y(x) + x + x
+--R /
+--R 4
+--R Type: Expression
Integer
+--E 23
+
+--S 24 of 120
+--Rode309 := (2*y(x)**3+y(x))*D(y(x),x)-2*x**3-x
+--R
+--R
+--R 3 , 3
+--R (24) (2y(x) + y(x))y (x) - 2x - x
+--R
+--R Type: Expression
Integer
+--E 24
+
+--S 25 of 120
+--Ryx:=solve(ode309,y,x)
+--R
+--R
+--R 4 2 4 2
+--R y(x) + y(x) - x - x
+--R (25) -----------------------
+--R 2
+--R Type: Union(Expression
Integer,...)
+--E 25
+
+--S 26 of 120
+--Rode309expr := (2*yx**3+yx)*D(yx,x)-2*x**3-x
+--R
+--R
+--R (26)
+--R 15 13 4 2 11
+--R 2y(x) + 7y(x) + (- 6x - 6x + 9)y(x)
+--R +
+--R 4 2 9 8 6 4 2 7
+--R (- 15x - 15x + 5)y(x) + (6x + 12x - 6x - 12x + 5)y(x)
+--R +
+--R 8 6 4 2 5
+--R (9x + 18x + 6x - 3x + 6)y(x)
+--R +
+--R 12 10 8 6 4 2 3
+--R (- 2x - 6x - 3x + 4x - x - 4x + 2)y(x)
+--R +
+--R 12 10 8 6 4 2
+--R (- x - 3x - 3x - x - 2x - 2x )y(x)
+--R *
+--R ,
+--R y (x)
+--R
+--R +
+--R 3 12 3 10 7 5 3 8
+--R (- 2x - x)y(x) + (- 6x - 3x)y(x) + (6x + 9x - 3x - 3x)y(x)
+--R +
+--R 7 5 3 6 11 9 7 5 3
4
+--R (12x + 18x + 4x - x)y(x) + (- 6x - 15x - 6x + 6x - x -
2x)y(x)
+--R +
+--R 11 9 7 5 3 2 15 13 11
9
+--R (- 6x - 15x - 12x - 3x - 4x - 2x)y(x) + 2x + 7x + 9x +
5x
+--R +
+--R 7 5 3
+--R 5x + 6x - 6x - 4x
+--R /
+--R 4
+--R Type: Expression
Integer
+--E 26
+
+--S 27 of 120
+--Rode310 := (2*y(x)**3+5*x**2*y(x))*D(y(x),x)+5*x*y(x)**2+x**3
+--R
+--R
+--R 3 2 , 2 3
+--R (27) (2y(x) + 5x y(x))y (x) + 5x y(x) + x
+--R
+--R Type: Expression
Integer
+--E 27
+
+--S 28 of 120
+--Ryx:=solve(ode310,y,x)
+--R
+--R
+--R 4 2 2 4
+--R 2y(x) + 10x y(x) + x
+--R (28) -----------------------
+--R 4
+--R Type: Union(Expression
Integer,...)
+--E 28
+
+--S 29 of 120
+--Rode310expr := (2*yx**3+5*x**2*yx)*D(yx,x)+5*x*yx**2+x**3
+--R
+--R
+--R (29)
+--R 15 2 13 4 11 6 9
+--R 16y(x) + 280x y(x) + 1824x y(x) + 5300x y(x)
+--R +
+--R 8 2 7 10 4 5
+--R (6212x + 160x )y(x) + (1590x + 1200x )y(x)
+--R +
+--R 12 6 3 14 8
+--R (152x + 2080x )y(x) + (5x + 200x )y(x)
+--R *
+--R ,
+--R y (x)
+--R
+--R +
+--R 14 3 12 5 10 7 8
+--R 40x y(x) + 608x y(x) + 3180x y(x) + (6212x + 40x)y(x)
+--R +
+--R 9 3 6 11 5 4 13 7 2
+--R (2650x + 800x )y(x) + (456x + 3120x )y(x) + (35x + 800x )y(x)
+--R +
+--R 15 9 3
+--R x + 50x + 32x
+--R /
+--R 32
+--R Type: Expression
Integer
+--E 29
+
+--S 30 of 120
+--Rode311 := (20*y(x)**3-3*x*y(x)**2+6*x**2*y(x)+3*x**3)*D(y(x),x)-_
+--R y(x)**3+6*x*y(x)**2+9*x**2*y(x)+4*x**3
+--R
+--R
+--R (30)
+--R 3 2 2 3 , 3 2 2
3
+--R (20y(x) - 3x y(x) + 6x y(x) + 3x )y (x) - y(x) + 6x y(x) + 9x y(x) +
4x
+--R
+--R Type: Expression
Integer
+--E 30
+
+--S 31 of 120
+--Ryx:=solve(ode311,y,x)
+--R
+--R
+--R 4 3 2 2 3 4
+--R (31) 5y(x) - x y(x) + 3x y(x) + 3x y(x) + x
+--R Type: Union(Expression
Integer,...)
+--E 31
+
+--S 32 of 120
+--Rode311expr := (20*yx**3-3*x*yx**2+6*x**2*yx+3*x**3)*D(yx,x)-_
+--R yx**3+6*x*yx**2+9*x**2*yx+4*x**3
+--R
+--R
+--R (32)
+--R 15 14 2 13 3 12
+--R 50000y(x) - 37500x y(x) + 115500x y(x) + 37700x y(x)
+--R +
+--R 4 11 5 2 10
+--R (67860x - 1500x)y(x) + (111540x + 825x )y(x)
+--R +
+--R 6 3 9 7 4 8
+--R (90600x - 2400x )y(x) + (72720x - 1206x )y(x)
+--R +
+--R 8 5 2 7 9 6 3 6
+--R (71880x - 1032x + 600x )y(x) + (52080x - 1554x - 210x )y(x)
+--R +
+--R 10 7 4 5 11 8 5 4
+--R (29880x - 1206x + 558x )y(x) + (17100x - 630x + 360x )y(x)
+--R +
+--R 12 9 6 3 3
+--R (8860x - 420x + 156x + 60x )y(x)
+--R +
+--R 13 10 7 4 2
+--R (3180x - 234x + 144x - 9x )y(x)
+--R +
+--R 14 11 8 5 15 12 9 6
+--R (660x - 72x + 90x + 18x )y(x) + 60x - 9x + 18x + 9x
+--R *
+--R ,
+--R y (x)
+--R
+--R +
+--R 15 14 2 13 3 12
+--R - 2500y(x) + 16500x y(x) + 8700x y(x) + (22620x - 125)y(x)
+--R +
+--R 4 11 5 2 10 6 3
9
+--R (50700x + 150x)y(x) + (54360x - 720x )y(x) + (56560x - 536x
)y(x)
+--R +
+--R 7 4 8 8 5 2 7
+--R (71880x - 645x + 150x)y(x) + (66960x - 1332x - 90x )y(x)
+--R +
+--R 9 6 3 6 10 7 4 5
+--R (49800x - 1407x + 372x )y(x) + (37620x - 1008x + 360x )y(x)
+--R +
+--R 11 8 5 2 4
+--R (26580x - 945x + 234x + 45x )y(x)
+--R +
+--R 12 9 6 3 3
+--R (13780x - 780x + 336x - 12x )y(x)
+--R +
+--R 13 10 7 4 2
+--R (4620x - 396x + 360x + 45x )y(x)
+--R +
+--R 14 11 8 5 15 12 9 6
3
+--R (900x - 108x + 162x + 54x )y(x) + 80x - 13x + 30x + 21x + 4x
+--R Type: Expression
Integer
+--E 32
+
+--S 33 of 120
+--Rode312 := (y(x)**2/b+x**2/a)*(y(x)*D(y(x),x)+x)+((a-b)/(a+b))*_
+--R (y(x)*D(y(x),x)-x)
+--R
+--R
+--R (33)
+--R 2 3 2 2 2 2 ,
+--R ((a b + a )y(x) + ((b + a b)x - a b + a b)y(x))y (x)
+--R
+--R +
+--R 2 2 2 3 2 2
+--R (a b + a )x y(x) + (b + a b)x + (a b - a b)x
+--R /
+--R 2 2
+--R a b + a b
+--R Type: Expression
Integer
+--E 33
+
+--S 34 of 120
+--Rsolve(ode312,y,x)
+--R
+--R
+--R (34) "failed"
+--R Type:
Union("failed",...)
+--E 34
+
+--S 35 of 120
+--Rode313 := (2*a*y(x)**3+3*a*x*y(x)**2-b*x**3+c*x**2)*D(y(x),x)-_
+--R a*y(x)**3+c*y(x)**2+3*b*x**2*y(x)+2*b*x**3
+--R
+--R
+--R (35)
+--R 3 2 3 2 , 3 2 2
+--R (2a y(x) + 3a x y(x) - b x + c x )y (x) - a y(x) + c y(x) + 3b x
y(x)
+--R
+--R +
+--R 3
+--R 2b x
+--R Type: Expression
Integer
+--E 35
+
+--S 36 of 120
+--Rsolve(ode313,y,x)
+--R
+--R
+--R (36) "failed"
+--R Type:
Union("failed",...)
+--E 36
+
+--S 37 of 120
+--Rode314 := x*y(x)**3*D(y(x),x)+y(x)**4-x*sin(x)
+--R
+--R
+--R 3 , 4
+--R (37) x y(x) y (x) - x sin(x) + y(x)
+--R
+--R Type: Expression
Integer
+--E 37
+
+--S 38 of 120
+--Ryx:=solve(ode314,y,x)
+--R
+--R
+--R 3 4 2 4 4
+--R (- 16x + 96x)sin(x) + (4x - 48x + 96)cos(x) + x y(x)
+--R (38) --------------------------------------------------------
+--R 4
+--R Type: Union(Expression
Integer,...)
+--E 38
+
+--S 39 of 120
+--Rode314expr := x*yx**3*D(yx,x)+yx**4-x*sin(x)
+--R
+--R
+--R (39)
+--R 14 12 10 8 3 3
+--R (- 16384x + 294912x - 1769472x + 3538944x )y(x) sin(x)
+--R +
+--R 15 13 11 9 7
+--R (12288x - 294912x + 2506752x - 8847360x + 10616832x
)
+--R *
+--R 3
+--R y(x) cos(x)
+--R +
+--R 15 13 11 7
+--R (3072x - 36864x + 110592x )y(x)
+--R *
+--R 2
+--R sin(x)
+--R +
+--R 16 14 12 10
8
+--R - 3072x + 92160x - 1032192x + 5308416x -
12386304x
+--R +
+--R 6
+--R 10616832x
+--R *
+--R 3 2
+--R y(x) cos(x)
+--R +
+--R 16 14 12 10 7
+--R (- 1536x + 27648x - 147456x + 221184x )y(x) cos(x)
+--R +
+--R 16 14 11
+--R (- 192x + 1152x )y(x)
+--R *
+--R sin(x)
+--R +
+--R 17 15 13 11 9
7
+--R 256x - 9216x + 129024x - 884736x + 3096576x -
5308416x
+--R +
+--R 5
+--R 3538944x
+--R *
+--R 3 3
+--R y(x) cos(x)
+--R +
+--R 17 15 13 11 9 7 2
+--R (192x - 4608x + 36864x - 110592x + 110592x )y(x) cos(x)
+--R +
+--R 17 15 13 11 17 15
+--R (48x - 576x + 1152x )y(x) cos(x) + 4x y(x)
+--R *
+--R ,
+--R y (x)
+--R
+--R +
+--R 14 12 10 8 6
+--R 16384x - 229376x + 196608x + 10616832x - 56623104x
+--R +
+--R 4
+--R 84934656x
+--R *
+--R 4
+--R sin(x)
+--R +
+--R 15 13 11 9 7
+--R - 12288x + 229376x - 540672x - 13959168x + 116785152x
+--R +
+--R 5 3
+--R - 339738624x + 339738624x
+--R *
+--R cos(x)
+--R +
+--R 15 13 11 9 7 4
+--R (- 3072x + 4096x + 479232x - 3538944x + 7077888x )y(x)
+--R *
+--R 3
+--R sin(x)
+--R +
+--R 16 14 12 10 8
+--R 3072x - 67584x + 147456x + 7372800x - 79626240x
+--R +
+--R 6 4 2
+--R 343277568x - 679477248x + 509607936x
+--R *
+--R 2
+--R cos(x)
+--R +
+--R 16 14 12 10 8
+--R 1536x - 3072x - 442368x + 4792320x - 17694720x
+--R +
+--R 6
+--R 21233664x
+--R *
+--R 4
+--R y(x) cos(x)
+--R +
+--R 16 14 12 10 8
+--R (192x + 3456x - 55296x + 165888x )y(x)
+--R *
+--R 2
+--R sin(x)
+--R +
+--R 17 15 13 11 9
+--R - 256x + 5120x + 43008x - 2064384x + 23445504x
+--R +
+--R 7 5 3
+--R - 129171456x + 378667008x - 566231040x + 339738624x
+--R *
+--R 3
+--R cos(x)
+--R +
+--R 17 15 13 11 9
+--R - 192x - 1536x + 147456x - 1953792x + 10506240x
+--R +
+--R 7 5
+--R - 24772608x + 21233664x
+--R *
+--R 4 2
+--R y(x) cos(x)
+--R +
+--R 17 15 13 11 9 8
+--R (- 48x - 1728x + 40320x - 221184x + 331776x )y(x) cos(x)
+--R +
+--R 17 15 13 12
+--R (- 4x - 256x + 1536x )y(x) - 256x
+--R *
+--R sin(x)
+--R +
+--R 16 14 12 10 8
6
+--R 256x - 12288x + 245760x - 2654208x + 16809984x -
63700992x
+--R +
+--R 4 2
+--R 141557760x - 169869312x + 84934656
+--R *
+--R 4
+--R cos(x)
+--R +
+--R 16 14 12 10 8
6
+--R 512x - 18432x + 258048x - 1769472x + 6193152x -
10616832x
+--R +
+--R 4
+--R 7077888x
+--R *
+--R 4 3
+--R y(x) cos(x)
+--R +
+--R 16 14 12 10 8 8 2
+--R (288x - 6912x + 55296x - 165888x + 165888x )y(x) cos(x)
+--R +
+--R 16 14 12 12 16 16
+--R (64x - 768x + 1536x )y(x) cos(x) + 5x y(x)
+--R /
+--R 256
+--R Type: Expression
Integer
+--E 39
+
+--S 40 of 120
+--Rode315 := (2*x*y(x)**3-x**4)*D(y(x),x)-y(x)**4+2*x**3*y(x)
+--R
+--R
+--R 3 4 , 4 3
+--R (40) (2x y(x) - x )y (x) - y(x) + 2x y(x)
+--R
+--R Type: Expression
Integer
+--E 40
+
+--S 41 of 120
+--Rsolve(ode315,y,x)
+--R
+--R
+--R (41) "failed"
+--R Type:
Union("failed",...)
+--E 41
+
+--S 42 of 120
+--Rode316 := (2*x*y(x)**3+y(x))*D(y(x),x)+2*y(x)**2
+--R
+--R
+--R 3 , 2
+--R (42) (2x y(x) + y(x))y (x) + 2y(x)
+--R
+--R Type: Expression
Integer
+--E 42
+
+--S 43 of 120
+--Ryx:=solve(ode316,y,x)
+--R
+--R
+--R 2
+--R y(x)
+--R ----- 2
+--R 2 y(x)
+--R 4x %e + Ei(-----)
+--R 2
+--R (43) ----------------------
+--R 2
+--R Type: Union(Expression
Integer,...)
+--E 43
+
+--S 44 of 120
+--Rode316expr := (2*x*yx**3+yx)*D(yx,x)+2*yx**2
+--R
+--R
+--R (44)
+--R 2 4
2 3
+--R y(x)
y(x)
+--R ----- 2
-----
+--R 5 2 4 2 4 2 3 y(x) 2
+--R (128x y(x) + 64x )(%e ) + (96x y(x) + 48x )Ei(-----)(%e
)
+--R 2
+--R +
+--R 2 2
+--R y(x)
+--R 2 2 -----
+--R 3 2 2 y(x) 2 2 2
+--R ((24x y(x) + 12x )Ei(-----) + 16x y(x) + 8x)(%e )
+--R 2
+--R +
+--R 2
+--R y(x)
+--R 2 3 2 -----
+--R 2 2 y(x) 2 y(x) 2
+--R ((2x y(x) + x)Ei(-----) + (4x y(x) + 2)Ei(-----))%e
+--R 2 2
+--R *
+--R ,
+--R y (x)
+--R
+--R +
+--R 2 4 2 3
+--R y(x) y(x)
+--R ----- 2 -----
+--R 4 2 3 y(x) 2
+--R 128x y(x)(%e ) + 96x y(x)Ei(-----)(%e )
+--R 2
+--R +
+--R 2 2
+--R y(x)
+--R 2 2 -----
+--R 2 y(x) 2 2
+--R (24x y(x)Ei(-----) + (32x + 16x)y(x))(%e )
+--R 2
+--R +
+--R 2
+--R y(x)
+--R 2 3 2 ----- 2 2
+--R y(x) y(x) 2 y(x)
+--R (2x y(x)Ei(-----) + (16x + 4)y(x)Ei(-----))%e + 2y(x)Ei(-----)
+--R 2 2 2
+--R /
+--R 4y(x)
+--R Type: Expression
Integer
+--E 44
+
+--S 45 of 120
+--Rode317 := (2*x*y(x)**3+x*y(x)+x**2)*D(y(x),x)+y(x)**2-x*y(x)
+--R
+--R
+--R 3 2 , 2
+--R (45) (2x y(x) + x y(x) + x )y (x) + y(x) - x y(x)
+--R
+--R Type: Expression
Integer
+--E 45
+
+--S 46 of 120
+--Rsolve(ode317,y,x)
+--R
+--R
+--R (46) "failed"
+--R Type:
Union("failed",...)
+--E 46
+
+--S 47 of 120
+--Rode318 := (3*x*y(x)**3-4*x*y(x)+y(x))*D(y(x),x)+y(x)**2*(y(x)**2-2)
+--R
+--R
+--R 3 , 4 2
+--R (47) (3x y(x) + (- 4x + 1)y(x))y (x) + y(x) - 2y(x)
+--R
+--R Type: Expression
Integer
+--E 47
+
+--S 48 of 120
+--Ryx:=solve(ode318,y,x)
+--R
+--R
+--R (48)
+--R +---------+
+--R 4 2 | 2 5
3
+--R (- x y(x) + (2x - 1)y(x) + 2)\|y(x) - 2 + x y(x) + (- 2x +
1)y(x)
+--R +
+--R - 2y(x)
+--R /
+--R +---------+
+--R | 2 2
+--R y(x)\|y(x) - 2 - y(x) + 2
+--R Type: Union(Expression
Integer,...)
+--E 48
+
+--S 49 of 120
+--Rode318expr := (3*x*yx**3-4*x*yx+yx)*D(yx,x)+yx**2*(yx**2-2)
+--R
+--R
+--R (49)
+--R 5 11 5 4 9 5 4 3 7
+--R 9x y(x) + (- 30x + 30x )y(x) + (24x - 96x + 36x )y(x)
+--R +
+--R 4 3 2 5 3 2 3
+--R (72x - 120x + 21x )y(x) + (88x - 68x + 7x)y(x)
+--R +
+--R 2
+--R (40x - 14x + 1)y(x)
+--R *
+--R ,
+--R y (x)
+--R
+--R +
+--R 4 12 4 3 10 4 3 2 8
+--R 4x y(x) + (- 16x + 13x )y(x) + (16x - 52x + 15x )y(x)
+--R +
+--R 3 2 6 2 4 2
+--R (52x - 66x + 8x)y(x) + (72x - 38x + 2)y(x) + (44x - 8)y(x) + 8
+--R Type: Expression
Integer
+--E 49
+
+--S 50 of 120
+--Rode319 := (7*x*y(x)**3+y(x)-5*x)*D(y(x),x)+y(x)**4-5*y(x)
+--R
+--R
+--R 3 , 4
+--R (50) (7x y(x) + y(x) - 5x)y (x) + y(x) - 5y(x)
+--R
+--R Type: Expression
Integer
+--E 50
+
+--S 51 of 120
+--Ryx:=solve(ode319,y,x)
+--R
+--R
+--R 7 5 4 2
+--R 10x y(x) + 2y(x) - 100x y(x) - 25y(x) + 250x y(x)
+--R (51) -----------------------------------------------------
+--R 10
+--R Type: Union(Expression
Integer,...)
+--E 51
+
+--S 52 of 120
+--Rode319expr := (7*x*yx**3+yx-5*x)*D(yx,x)+yx**4-5*yx
+--R
+--R
+--R (52)
+--R 5 27 4 25 5 24 3
23
+--R 490000x y(x) + 364000x y(x) - 17500000x y(x) + 100800x y(x)
+--R +
+--R 4 22 5 2 21 3
20
+--R - 13685000x y(x) + (269500000x + 12320x )y(x) - 3969000x
y(x)
+--R +
+--R 4 19 5 2 18
+--R (210000000x + 560x)y(x) + (- 2327500000x - 505400x )y(x)
+--R +
+--R 3 17 4 16
+--R 60952500x y(x) + (- 1710625000x - 23800x)y(x)
+--R +
+--R 5 2 15 3 14
+--R (12250000000x + 7784000x )y(x) - 464625000x y(x)
+--R +
+--R 4 2 13
+--R (7962500000x + 70000x + 367500x)y(x)
+--R +
+--R 5 2 12 3
11
+--R (- 39812500000x - 55168750x )y(x) + (1842750000x +
24000x)y(x)
+--R +
+--R 4 2 10
+--R (- 20934375000x - 1100000x - 2406250x)y(x)
+--R +
+--R 5 2 9
+--R (76562500000x + 175000000x + 2000)y(x)
+--R +
+--R 3 8
+--R (- 3543750000x - 405000x)y(x)
+--R +
+--R 4 2 7
+--R (28000000000x + 6000000x + 5468750x)y(x)
+--R +
+--R 5 2 6
+--R (- 76562500000x - 191756250x - 35000)y(x)
+--R +
+--R 3 5
+--R (2460937500x + 1800000x)y(x)
+--R +
+--R 4 2 4
+--R (- 13671875000x - 12500000x - 50000x)y(x)
+--R +
+--R 5 2 3 2
+--R (27343750000x + 2000000x + 125000)y(x) - 1875000x y(x)
+--R +
+--R 2 2
+--R (6250000x + 250000x)y(x) - 1250000x
+--R *
+--R ,
+--R y (x)
+--R
+--R +
+--R 4 28 3 26 4 25 2 24
+--R 80000x y(x) + 50000x y(x) - 3200000x y(x) + 10800x y(x)
+--R +
+--R 3 23 4 22 2 21
+--R - 2125000x y(x) + (56000000x + 880x)y(x) - 486000x y(x)
+--R +
+--R 3 20 4 19
+--R (37500000x + 16)y(x) + (- 560000000x - 41800x)y(x)
+--R +
+--R 2 18 3 17
+--R 8707500x y(x) + (- 359375000x - 800)y(x)
+--R +
+--R 4 16 2 15
+--R (3500000000x + 764500x)y(x) - 79650000x y(x)
+--R +
+--R 3 14
+--R (2031250000x + 10000x + 15000)y(x)
+--R +
+--R 4 13 2 12
+--R (- 14000000000x - 6668750x)y(x) + (394875000x + 2000)y(x)
+--R +
+--R 3 11
+--R (- 6796875000x - 200000x - 125000)y(x)
+--R +
+--R 4 10 2 9
+--R (35000000000x + 27500000x)y(x) + (- 1012500000x - 45000)y(x)
+--R +
+--R 3 8
+--R (12500000000x + 1500000x + 390625)y(x)
+--R +
+--R 4 7 2 6
+--R (- 50000000000x - 43068750x)y(x) + (1054687500x + 300000)y(x)
+--R +
+--R 3 5
+--R (- 9765625000x - 5000000x - 10000)y(x)
+--R +
+--R 4 4 3
2
+--R (31250000000x + 1000000x)y(x) - 625000y(x) + (6250000x +
125000)y(x)
+--R +
+--R - 2500000x y(x)
+--R /
+--R 10000
+--R Type: Expression
Integer
+--E 52
+
+--S 53 of 120
+--Rode320 := (x**2*y(x)**3+x*y(x))*D(y(x),x)-1
+--R
+--R
+--R 2 3 ,
+--R (53) (x y(x) + x y(x))y (x) - 1
+--R
+--R Type: Expression
Integer
+--E 53
+
+--S 54 of 120
+--Rsolve(ode320,y,x)
+--R
+--R
+--R (54) "failed"
+--R Type:
Union("failed",...)
+--E 54
+
+--S 55 of 120
+--Rode321 := (2*x**2*y(x)**3+x**2*y(x)**2-2*x)*D(y(x),x)-2*y(x)-1
+--R
+--R
+--R 2 3 2 2 ,
+--R (55) (2x y(x) + x y(x) - 2x)y (x) - 2y(x) - 1
+--R
+--R Type: Expression
Integer
+--E 55
+
+--S 56 of 120
+--Rsolve(ode321,y,x)
+--R
+--R
+--R (56) "failed"
+--R Type:
Union("failed",...)
+--E 56
+
+--S 57 of 120
+--Rode322 := (10*x**2*y(x)**3-3*y(x)**2-2)*D(y(x),x)+5*x*y(x)**4+x
+--R
+--R
+--R 2 3 2 , 4
+--R (57) (10x y(x) - 3y(x) - 2)y (x) + 5x y(x) + x
+--R
+--R Type: Expression
Integer
+--E 57
+
+--S 58 of 120
+--Ryx:=solve(ode322,y,x)
+--R
+--R
+--R 2 4 3 2
+--R 5x y(x) - 2y(x) - 4y(x) + x
+--R (58) ------------------------------
+--R 2
+--R Type: Union(Expression
Integer,...)
+--E 58
+
+--S 59 of 120
+--Rode322expr := (10*x**2*yx**3-3*yx**2-2)*D(yx,x)+5*x*yx**4+x
+--R
+--R
+--R (59)
+--R 10 15 8 14 6 13
+--R 25000x y(x) - 37500x y(x) + 21000x y(x)
+--R +
+--R 8 4 12 10 6 2 11
+--R (- 65000x - 5200x )y(x) + (15000x + 69000x + 480x )y(x)
+--R +
+--R 8 4 10 6 2 9
+--R (- 16500x - 23100x )y(x) + (66000x + 2000x )y(x)
+--R +
+--R 8 4 8 10 6 2
7
+--R (- 27000x - 38520x + 144)y(x) + (3000x + 18000x + 3840x
)y(x)
+--R +
+--R 8 4 6 6 2 5
+--R (- 2100x - 24920x + 672)y(x) + (14760x + 4656x )y(x)
+--R +
+--R 8 4 4 10 6 2 3
+--R (- 3000x - 3600x + 960)y(x) + (200x + 840x + 1856x )y(x)
+--R +
+--R 8 4 2 6 2 8 4
+--R (- 60x - 1884x + 480)y(x) + (480x - 192x )y(x) - 40x + 24x +
64
+--R *
+--R ,
+--R y (x)
+--R
+--R +
+--R 9 16 7 15 5 14 7 3
13
+--R 15625x y(x) - 20000x y(x) + 9000x y(x) + (- 40000x - 1600x
)y(x)
+--R +
+--R 9 5 12 7 3 11
+--R (12500x + 34500x + 80x)y(x) + (- 12000x - 8400x )y(x)
+--R +
+--R 5 10 7 3 9
+--R (39600x + 400x)y(x) + (- 24000x - 17120x )y(x)
+--R +
+--R 9 5 8 7 3 7
+--R (3750x + 13500x + 960x)y(x) + (- 2400x - 14240x )y(x)
+--R +
+--R 5 6 7 3 5
+--R (14760x + 1552x)y(x) + (- 4800x - 2880x )y(x)
+--R +
+--R 9 5 4 7 3 3
+--R (500x + 1260x + 928x)y(x) + (- 160x - 2512x )y(x)
+--R +
+--R 5 2 7 3 9 5
+--R (1440x - 192x)y(x) + (- 320x + 96x )y(x) + 25x - 12x - 16x
+--R /
+--R 16
+--R Type: Expression
Integer
+--E 59
+
+--S 60 of 120
+--Rode323 := (a*x*y(x)**3+c)*x*D(y(x),x)+(b*x**3*y(x)+c)*y(x)
+--R
+--R
+--R 2 3 , 3 2
+--R (60) (a x y(x) + c x)y (x) + b x y(x) + c y(x)
+--R
+--R Type: Expression
Integer
+--E 60
+
+--S 61 of 120
+--Rsolve(ode323,y,x)
+--R
+--R
+--R (61) "failed"
+--R Type:
Union("failed",...)
+--E 61
+
+--S 62 of 120
+--Rode324 := (2*x**3*y(x)**3-x)*D(y(x),x)+2*x**3*y(x)**3-y(x)
+--R
+--R
+--R 3 3 , 3 3
+--R (62) (2x y(x) - x)y (x) + 2x y(x) - y(x)
+--R
+--R Type: Expression
Integer
+--E 62
+
+--S 63 of 120
+--Rsolve(ode324,y,x)
+--R
+--R
+--R (63) "failed"
+--R Type:
Union("failed",...)
+--E 63
+
+--S 64 of 120
+--Rode325 := y(x)*(y(x)**3-2*x**3)*D(y(x),x)+(2*y(x)**3-x**3)*x
+--R
+--R
+--R 4 3 , 3 4
+--R (64) (y(x) - 2x y(x))y (x) + 2x y(x) - x
+--R
+--R Type: Expression
Integer
+--E 64
+
+--S 65 of 120
+--Rsolve(ode325,y,x)
+--R
+--R
+--R (65) "failed"
+--R Type:
Union("failed",...)
+--E 65
+
+--S 66 of 120
+--Rode326 :=
y(x)*((a*y(x)+b*x)**3+b*x**3)*D(y(x),x)+x*((a*y(x)+b*x)**3+a*y(x)**3)
+--R
+--R
+--R (66)
+--R 3 4 2 3 2 2 2 3 3 ,
+--R (a y(x) + 3a b x y(x) + 3a b x y(x) + (b + b)x y(x))y (x)
+--R
+--R +
+--R 3 3 2 2 2 2 3 3 4
+--R (a + a)x y(x) + 3a b x y(x) + 3a b x y(x) + b x
+--R Type: Expression
Integer
+--E 66
+
+--S 67 of 120
+--Rsolve(ode326,y,x)
+--R
+--R
+--R (67) "failed"
+--R Type:
Union("failed",...)
+--E 67
+
+--S 68 of 120
+--Rode327 := (x*y(x)**4+2*x**2*y(x)**3+2*y(x)+x)*D(y(x),x)+y(x)**5+y(x)
+--R
+--R
+--R 4 2 3 , 5
+--R (68) (x y(x) + 2x y(x) + 2y(x) + x)y (x) + y(x) + y(x)
+--R
+--R Type: Expression
Integer
+--E 68
+
+--S 69 of 120
+--Rsolve(ode327,y,x)
+--R
+--R
+--R (69) "failed"
+--R Type:
Union("failed",...)
+--E 69
+
+--S 70 of 120
+--Rode328 := a*x**2*y(x)**n*D(y(x),x)-2*x*D(y(x),x)+y(x)
+--R
+--R
+--R 2 n ,
+--R (70) (a x y(x) - 2x)y (x) + y(x)
+--R
+--R Type: Expression
Integer
+--E 70
+
+--S 71 of 120
+--Rsolve(ode328,y,x)
+--R
+--R
+--R (71) "failed"
+--R Type:
Union("failed",...)
+--E 71
+
+--S 72 of 120
+--Rode329 := y(x)**m*x**n*(a*x*D(y(x),x)+b*y(x))+alpha*x*D(y(x),x)+beta*y(x)
+--R
+--R
+--R n m , n m
+--R (72) (a x x y(x) + alpha x)y (x) + b y(x)x y(x) + beta y(x)
+--R
+--R Type: Expression
Integer
+--E 72
+
+--S 73 of 120
+--Rsolve(ode329,y,x)
+--R
+--R
+--R (73) "failed"
+--R Type:
Union("failed",...)
+--E 73
+
+--S 74 of 120
+--Rode330 := (f(x+y(x))+1)*D(y(x),x)+f(x+y(x))
+--R
+--R
+--R ,
+--R (74) (f(y(x) + x) + 1)y (x) + f(y(x) + x)
+--R
+--R Type: Expression
Integer
+--E 74
+
+--S 75 of 120
+--Rsolve(ode330,y,x)
+--R
+--R
+--R >> Error detected within library code:
+--R Sorry - cannot handle that integrand yet
+--R
+--R Continuing to read the file...
+--R
+--E 75
+
+@
+I have no idea what to do with this
+\begin{verbatim}
+ ode331 := D(y(x),x)*convert([sum(f[nu](x)*y(x)**nu,'nu'=1..p)],`+`)-_
+ convert([sum(g[nu](x)*y(x)**nu,'nu'=1..q)],`+`)
+\end{verbatim}
+<<*>>=
+--R
+--S 76 of 120
+--Rode333 := (2*x**(5/2)*y(x)**(3/2)+x**2*y(x)-x)*D(y(x),x)-_
+--R x**(3/2)*y(x)**(5/2)+x*y(x)**2-y(x)
+--R
+--R
+--R (75)
+--R 2 +-+ +----+ 2 , 2 +-+ +----+ 2
+--R (2x y(x)\|x \|y(x) + x y(x) - x)y (x) - x y(x) \|x \|y(x) + x y(x) -
y(x)
+--R
+--R Type: Expression
Integer
+--E 76
+
+--S 77 of 120
+--Rsolve(ode333,y,x)
+--R
+--R
+--R (76) "failed"
+--R Type:
Union("failed",...)
+--E 77
+
+--S 78 of 120
+--Rode334 := (sqrt(y(x)+x)+1)*D(y(x),x)+1
+--R
+--R
+--R +--------+ ,
+--R (77) (\|y(x) + x + 1)y (x) + 1
+--R
+--R Type: Expression
Integer
+--E 78
+
+--S 79 of 120
+--Rsolve(ode334,y,x)
+--R
+--R
+--R (78) "failed"
+--R Type:
Union("failed",...)
+--E 79
+
+--S 80 of 120
+--Rode335 := sqrt(y(x)**2-1)*D(y(x),x)-sqrt(x**2-1)
+--R
+--R
+--R +---------+ +------+
+--R | 2 , | 2
+--R (79) \|y(x) - 1 y (x) - \|x - 1
+--R
+--R Type: Expression
Integer
+--E 80
+
+--S 81 of 120
+--Ryx:=solve(ode335,y,x)
+--R
+--R
+--R (80)
+--R +------+ +---------+
+--R | 2 2 | 2
+--R (4x y(x)\|x - 1 + (- 4x + 2)y(x))\|y(x) - 1
+--R +
+--R +------+
+--R 2 | 2 2 2 2
+--R (- 4x y(x) + 2x)\|x - 1 + (4x - 2)y(x) - 2x + 1
+--R *
+--R +---------+
+--R | 2
+--R log(\|y(x) - 1 - y(x))
+--R +
+--R +------+ +------+
+--R | 2 2 | 2
+--R (- 4x y(x)\|x - 1 + (4x - 2)y(x))log(\|x - 1 - x)
+--R +
+--R +------+
+--R 3 3 | 2 2 3
+--R (- 4x y(x) + 4x y(x))\|x - 1 + (4x - 2)y(x)
+--R +
+--R 4 2
+--R (- 4x + 2x + 1)y(x)
+--R *
+--R +---------+
+--R | 2
+--R \|y(x) - 1
+--R +
+--R +------+ +------+
+--R 2 | 2 2 2 2 | 2
+--R ((4x y(x) - 2x)\|x - 1 + (- 4x + 2)y(x) + 2x - 1)log(\|x - 1
- x)
+--R +
+--R +------+
+--R 4 3 2 3 | 2 2 4
+--R (4x y(x) + (- 4x - 2x)y(x) + 2x - x)\|x - 1 + (- 4x + 2)y(x)
+--R +
+--R 4 2 4 2
+--R (4x - 2)y(x) - 2x + 2x
+--R /
+--R +------+ +---------+
+--R | 2 2 | 2
+--R (8x y(x)\|x - 1 + (- 8x + 4)y(x))\|y(x) - 1
+--R +
+--R +------+
+--R 2 | 2 2 2 2
+--R (- 8x y(x) + 4x)\|x - 1 + (8x - 4)y(x) - 4x + 2
+--R Type: Union(Expression
Integer,...)
+--E 81
+
+--S 82 of 120
+--Rode335expr := sqrt(yx**2-1)*D(yx,x)-sqrt(x**2-1)
+--R
+--R
+--R (81)
+--R 4 2 5 4 2 3
+--R (- 64x + 64x - 8)y(x) + (96x - 96x + 12)y(x)
+--R +
+--R 4 2
+--R (- 32x + 32x - 4)y(x)
+--R *
+--R +------+
+--R | 2
+--R \|x - 1
+--R +
+--R 5 3 5 5 3 3
+--R (64x - 96x + 32x)y(x) + (- 96x + 144x - 48x)y(x)
+--R +
+--R 5 3
+--R (32x - 48x + 16x)y(x)
+--R *
+--R +---------+
+--R | 2
+--R \|y(x) - 1
+--R +
+--R 4 2 6 4 2 4
+--R (64x - 64x + 8)y(x) + (- 128x + 128x - 16)y(x)
+--R +
+--R 4 2 2 4 2
+--R (72x - 72x + 9)y(x) - 8x + 8x - 1
+--R *
+--R +------+
+--R | 2
+--R \|x - 1
+--R +
+--R 5 3 6 5 3 4
+--R (- 64x + 96x - 32x)y(x) + (128x - 192x + 64x)y(x)
+--R +
+--R 5 3 2 5 3
+--R (- 72x + 108x - 36x)y(x) + 8x - 12x + 4x
+--R *
+--R ,
+--R y (x)
+--R
+--R +
+--R 5 3 4 5 3 2
5
+--R (64x - 96x + 32x)y(x) + (- 64x + 96x - 32x)y(x) +
8x
+--R +
+--R 3
+--R - 12x + 4x
+--R *
+--R +------+
+--R | 2
+--R \|x - 1
+--R +
+--R 6 4 2 4 6 4 2
2
+--R (- 64x + 128x - 72x + 8)y(x) + (64x - 128x + 72x -
8)y(x)
+--R +
+--R 6 4 2
+--R - 8x + 16x - 9x + 1
+--R *
+--R +---------+
+--R | 2
+--R \|y(x) - 1
+--R +
+--R 5 3 5 5 3 3
+--R (- 64x + 96x - 32x)y(x) + (96x - 144x + 48x)y(x)
+--R +
+--R 5 3
+--R (- 32x + 48x - 16x)y(x)
+--R *
+--R +------+
+--R | 2
+--R \|x - 1
+--R +
+--R 6 4 2 5 6 4 2
3
+--R (64x - 128x + 72x - 8)y(x) + (- 96x + 192x - 108x +
12)y(x)
+--R +
+--R 6 4 2
+--R (32x - 64x + 36x - 4)y(x)
+--R *
+--R ROOT
+--R +------+
+--R 3 3 3 | 2
+--R ((64x - 32x)y(x) + (- 32x + 16x)y(x))\|x - 1
+--R +
+--R 4 2 3 4 2
+--R (- 64x + 64x - 8)y(x) + (32x - 32x + 4)y(x)
+--R *
+--R +---------+
+--R | 2
+--R \|y(x) - 1
+--R +
+--R 3 4 3 2 3
+--R ((- 64x + 32x)y(x) + (64x - 32x)y(x) - 8x + 4x)
+--R *
+--R +------+
+--R | 2
+--R \|x - 1
+--R +
+--R 4 2 4 4 2 2 4
+--R (64x - 64x + 8)y(x) + (- 64x + 64x - 8)y(x) + 8x
+--R +
+--R 2
+--R - 8x + 1
+--R *
+--R +---------+ 2
+--R | 2
+--R log(\|y(x) - 1 - y(x))
+--R +
+--R
+------+
+--R 3 3 3 | 2
+--R ((- 128x + 64x)y(x) + (64x - 32x)y(x))\|x -
1
+--R +
+--R 4 2 3 4 2
+--R (128x - 128x + 16)y(x) + (- 64x + 64x -
8)y(x)
+--R *
+--R +------+
+--R | 2
+--R log(\|x - 1 - x)
+--R +
+--R 3 5 5 3
+--R (- 128x + 64x)y(x) + (128x - 48x)y(x)
+--R +
+--R 5 3
+--R (- 64x + 48x )y(x)
+--R *
+--R +------+
+--R | 2
+--R \|x - 1
+--R +
+--R 4 2 5
+--R (128x - 128x + 16)y(x)
+--R +
+--R 6 4 2 3
+--R (- 128x + 64x + 64x - 16)y(x)
+--R +
+--R 6 4 2
+--R (64x - 80x + 16x + 2)y(x)
+--R *
+--R +---------+
+--R | 2
+--R \|y(x) - 1
+--R +
+--R 3 4 3 2
3
+--R (128x - 64x)y(x) + (- 128x + 64x)y(x) +
16x
+--R +
+--R - 8x
+--R *
+--R +------+
+--R | 2
+--R \|x - 1
+--R +
+--R 4 2 4 4 2
2
+--R (- 128x + 128x - 16)y(x) + (128x - 128x +
16)y(x)
+--R +
+--R 4 2
+--R - 16x + 16x - 2
+--R *
+--R +------+
+--R | 2
+--R log(\|x - 1 - x)
+--R +
+--R 3 6 5 3 4
+--R (128x - 64x)y(x) + (- 128x - 64x + 80x)y(x)
+--R +
+--R 5 3 2 5 3
+--R (128x - 64x - 16x)y(x) - 16x + 16x - 2x
+--R *
+--R +------+
+--R | 2
+--R \|x - 1
+--R +
+--R 4 2 6 6 2 4
+--R (- 128x + 128x - 16)y(x) + (128x - 128x + 24)y(x)
+--R +
+--R 6 4 2 6 4 2
+--R (- 128x + 128x - 8)y(x) + 16x - 24x + 8x
+--R *
+--R +---------+
+--R | 2
+--R log(\|y(x) - 1 - y(x))
+--R +
+--R +------+
+--R 3 3 3 | 2
+--R ((64x - 32x)y(x) + (- 32x + 16x)y(x))\|x - 1
+--R +
+--R 4 2 3 4 2
+--R (- 64x + 64x - 8)y(x) + (32x - 32x + 4)y(x)
+--R *
+--R +------+ 2
+--R | 2
+--R log(\|x - 1 - x)
+--R +
+--R 3 5 5 3
+--R (128x - 64x)y(x) + (- 128x + 48x)y(x)
+--R +
+--R 5 3
+--R (64x - 48x )y(x)
+--R *
+--R +------+
+--R | 2
+--R \|x - 1
+--R +
+--R 4 2 5
+--R (- 128x + 128x - 16)y(x)
+--R +
+--R 6 4 2 3
+--R (128x - 64x - 64x + 16)y(x)
+--R +
+--R 6 4 2
+--R (- 64x + 80x - 16x - 2)y(x)
+--R *
+--R +------+
+--R | 2
+--R log(\|x - 1 - x)
+--R +
+--R 3 7 5 3 5
+--R (64x - 32x)y(x) + (- 128x + 32x + 32x)y(x)
+--R +
+--R 7 5 3 3
+--R (64x + 32x - 320x + 128x)y(x)
+--R +
+--R 7 5 3
+--R (- 32x + 32x + 128x - 66x)y(x)
+--R *
+--R +------+
+--R | 2
+--R \|x - 1
+--R +
+--R 4 2 7 6 4 2
5
+--R (- 64x + 64x - 8)y(x) + (128x - 96x - 32x +
12)y(x)
+--R +
+--R 8 4 2 3
+--R (- 64x + 344x - 280x + 28)y(x)
+--R +
+--R 8 6 4 2
+--R (32x - 48x - 116x + 132x - 16)y(x)
+--R *
+--R +---------+
+--R | 2
+--R \|y(x) - 1
+--R +
+--R 3 4 3 2 3
+--R ((- 64x + 32x)y(x) + (64x - 32x)y(x) - 8x + 4x)
+--R *
+--R +------+
+--R | 2
+--R \|x - 1
+--R +
+--R 4 2 4 4 2 2 4
+--R (64x - 64x + 8)y(x) + (- 64x + 64x - 8)y(x) + 8x
+--R +
+--R 2
+--R - 8x + 1
+--R *
+--R +------+ 2
+--R | 2
+--R log(\|x - 1 - x)
+--R +
+--R 3 6 5 3 4
+--R (- 128x + 64x)y(x) + (128x + 64x - 80x)y(x)
+--R +
+--R 5 3 2 5 3
+--R (- 128x + 64x + 16x)y(x) + 16x - 16x + 2x
+--R *
+--R +------+
+--R | 2
+--R \|x - 1
+--R +
+--R 4 2 6 6 2 4
+--R (128x - 128x + 16)y(x) + (- 128x + 128x - 24)y(x)
+--R +
+--R 6 4 2 6 4 2
+--R (128x - 128x + 8)y(x) - 16x + 24x - 8x
+--R *
+--R +------+
+--R | 2
+--R log(\|x - 1 - x)
+--R +
+--R 3 8 5 6
+--R (- 64x + 32x)y(x) + (128x - 48x)y(x)
+--R +
+--R 7 5 3 4
+--R (- 64x - 96x + 344x - 116x)y(x)
+--R +
+--R 7 5 3 2 7 5 3
+--R (64x - 32x - 280x + 132x)y(x) - 8x + 12x + 28x -
16x
+--R *
+--R +------+
+--R | 2
+--R \|x - 1
+--R +
+--R 4 2 8 6 4 2 6
+--R (64x - 64x + 8)y(x) + (- 128x + 64x + 64x - 16)y(x)
+--R +
+--R 8 6 4 2 4
+--R (64x + 64x - 400x + 272x - 23)y(x)
+--R +
+--R 8 6 4 2 2 8 6
4
+--R (- 64x + 64x + 272x - 272x + 31)y(x) + 8x - 16x - 23x
+--R +
+--R 2
+--R 31x - 4
+--R /
+--R +------+
+--R 3 3 3 | 2
+--R ((256x - 128x)y(x) + (- 128x + 64x)y(x))\|x - 1
+--R +
+--R 4 2 3 4 2
+--R (- 256x + 256x - 32)y(x) + (128x - 128x + 16)y(x)
+--R *
+--R +---------+
+--R | 2
+--R \|y(x) - 1
+--R +
+--R 3 4 3 2 3
+--R ((- 256x + 128x)y(x) + (256x - 128x)y(x) - 32x + 16x)
+--R *
+--R +------+
+--R | 2
+--R \|x - 1
+--R +
+--R 4 2 4 4 2 2
4
+--R (256x - 256x + 32)y(x) + (- 256x + 256x - 32)y(x) +
32x
+--R +
+--R 2
+--R - 32x + 4
+--R +
+--R 5 3 4 5 3 2 5
+--R (64x - 96x + 32x)y(x) + (- 64x + 96x - 32x)y(x) + 8x
+--R +
+--R 3
+--R - 12x + 4x
+--R *
+--R +------+
+--R | 2
+--R \|x - 1
+--R +
+--R 6 4 2 4 6 4 2 2
+--R (- 64x + 128x - 72x + 8)y(x) + (64x - 128x + 72x - 8)y(x)
+--R +
+--R 6 4 2
+--R - 8x + 16x - 9x + 1
+--R *
+--R +---------+
+--R | 2
+--R \|y(x) - 1
+--R +
+--R 5 3 5 5 3 3
+--R (- 64x + 96x - 32x)y(x) + (96x - 144x + 48x)y(x)
+--R +
+--R 5 3
+--R (- 32x + 48x - 16x)y(x)
+--R *
+--R +------+
+--R | 2
+--R \|x - 1
+--R +
+--R 6 4 2 5 6 4 2 3
+--R (64x - 128x + 72x - 8)y(x) + (- 96x + 192x - 108x + 12)y(x)
+--R +
+--R 6 4 2
+--R (32x - 64x + 36x - 4)y(x)
+--R /
+--R 4 2 4 4 2 2 4 2
+--R ((64x - 64x + 8)y(x) + (- 64x + 64x - 8)y(x) + 8x - 8x
+ 1)
+--R *
+--R +------+
+--R | 2
+--R \|x - 1
+--R +
+--R 5 3 4 5 3 2 5 3
+--R (- 64x + 96x - 32x)y(x) + (64x - 96x + 32x)y(x) - 8x + 12x
- 4x
+--R *
+--R +---------+
+--R | 2
+--R \|y(x) - 1
+--R +
+--R 4 2 5 4 2 3
+--R (- 64x + 64x - 8)y(x) + (96x - 96x + 12)y(x)
+--R +
+--R 4 2
+--R (- 32x + 32x - 4)y(x)
+--R *
+--R +------+
+--R | 2
+--R \|x - 1
+--R +
+--R 5 3 5 5 3 3
+--R (64x - 96x + 32x)y(x) + (- 96x + 144x - 48x)y(x)
+--R +
+--R 5 3
+--R (32x - 48x + 16x)y(x)
+--R Type: Expression
Integer
+--E 82
+
+--S 83 of 120
+--Rode336 := (sqrt(y(x)**2+1)+a*x)*D(y(x),x)+sqrt(x**2+1)+a*y(x)
+--R
+--R
+--R +---------+ +------+
+--R | 2 , | 2
+--R (82) (\|y(x) + 1 + a x)y (x) + \|x + 1 + a y(x)
+--R
+--R Type: Expression
Integer
+--E 83
+
+--S 84 of 120
+--Ryx:=solve(ode336,y,x)
+--R
+--R
+--R (83)
+--R +------+ +---------+
+--R | 2 2 | 2
+--R (- 4x y(x)\|x + 1 + (4x + 2)y(x))\|y(x) + 1
+--R +
+--R +------+
+--R 2 | 2 2 2 2
+--R (4x y(x) + 2x)\|x + 1 + (- 4x - 2)y(x) - 2x - 1
+--R *
+--R +---------+
+--R | 2
+--R log(\|y(x) + 1 - y(x))
+--R +
+--R +------+ +------+
+--R | 2 2 | 2
+--R (- 4x y(x)\|x + 1 + (4x + 2)y(x))log(\|x + 1 - x)
+--R +
+--R +------+
+--R 3 2 2 3 | 2
+--R (- 4x y(x) + 8a x y(x) + (- 4x - 4x)y(x))\|x + 1
+--R +
+--R 2 3 3 2 4 2
+--R (4x + 2)y(x) + (- 8a x - 4a x)y(x) + (4x + 6x + 1)y(x)
+--R *
+--R +---------+
+--R | 2
+--R \|y(x) + 1
+--R +
+--R +------+ +------+
+--R 2 | 2 2 2 2 | 2
+--R ((4x y(x) + 2x)\|x + 1 + (- 4x - 2)y(x) - 2x - 1)log(\|x + 1
- x)
+--R +
+--R
+------+
+--R 4 2 3 3 2 2 3 | 2
+--R (4x y(x) - 8a x y(x) + (4x + 6x)y(x) - 4a x y(x) + 2x + x)\|x
+ 1
+--R +
+--R 2 4 3 3 4 2 2
+--R (- 4x - 2)y(x) + (8a x + 4a x)y(x) + (- 4x - 8x - 2)y(x)
+--R +
+--R 3 4 2
+--R (4a x + 2a x)y(x) - 2x - 2x
+--R /
+--R +------+ +---------+
+--R | 2 2 | 2
+--R (8x y(x)\|x + 1 + (- 8x - 4)y(x))\|y(x) + 1
+--R +
+--R +------+
+--R 2 | 2 2 2 2
+--R (- 8x y(x) - 4x)\|x + 1 + (8x + 4)y(x) + 4x + 2
+--R Type: Union(Expression
Integer,...)
+--E 84
+
+--S 85 of 120
+--Rode336expr := (sqrt(yx**2+1)+a*x)*D(yx,x)+sqrt(x**2+1)+a*yx
+--R
+--R
+--R (84)
+--R 6 4 2 7
+--R (- 2048x - 3072x - 1152x - 64)y(x)
+--R +
+--R 7 5 3 6
+--R (2048a x + 3072a x + 1152a x + 64a x)y(x)
+--R +
+--R 6 4 2 5
+--R (- 4096x - 6144x - 2304x - 128)y(x)
+--R +
+--R 7 5 3 4
+--R (3072a x + 4608a x + 1728a x + 96a x)y(x)
+--R +
+--R 6 4 2 3
+--R (- 2432x - 3648x - 1368x - 76)y(x)
+--R +
+--R 7 5 3 2
+--R (1152a x + 1728a x + 648a x + 36a x)y(x)
+--R +
+--R 6 4 2 7 5
+--R (- 384x - 576x - 216x - 12)y(x) + 64a x + 96a x
+--R +
+--R 3
+--R 36a x + 2a x
+--R *
+--R +------+
+--R | 2
+--R \|x + 1
+--R +
+--R 7 5 3 7
+--R (2048x + 4096x + 2432x + 384x)y(x)
+--R +
+--R 8 6 4 2 6
+--R (- 2048a x - 4096a x - 2432a x - 384a x )y(x)
+--R +
+--R 7 5 3 5
+--R (4096x + 8192x + 4864x + 768x)y(x)
+--R +
+--R 8 6 4 2 4
+--R (- 3072a x - 6144a x - 3648a x - 576a x )y(x)
+--R +
+--R 7 5 3 3
+--R (2432x + 4864x + 2888x + 456x)y(x)
+--R +
+--R 8 6 4 2 2
+--R (- 1152a x - 2304a x - 1368a x - 216a x )y(x)
+--R +
+--R 7 5 3 8 6
4
+--R (384x + 768x + 456x + 72x)y(x) - 64a x - 128a x -
76a x
+--R +
+--R 2
+--R - 12a x
+--R *
+--R +---------+
+--R | 2
+--R \|y(x) + 1
+--R +
+--R 6 4 2 8
+--R (2048x + 3072x + 1152x + 64)y(x)
+--R +
+--R 7 5 3 7
+--R (- 2048a x - 3072a x - 1152a x - 64a x)y(x)
+--R +
+--R 6 4 2 6
+--R (5120x + 7680x + 2880x + 160)y(x)
+--R +
+--R 7 5 3 5
+--R (- 4096a x - 6144a x - 2304a x - 128a x)y(x)
+--R +
+--R 6 4 2 4
+--R (4224x + 6336x + 2376x + 132)y(x)
+--R +
+--R 7 5 3 3
+--R (- 2432a x - 3648a x - 1368a x - 76a x)y(x)
+--R +
+--R 6 4 2 2
+--R (1216x + 1824x + 684x + 38)y(x)
+--R +
+--R 7 5 3 6 4
+--R (- 384a x - 576a x - 216a x - 12a x)y(x) + 64x + 96x
+--R +
+--R 2
+--R 36x + 2
+--R *
+--R +------+
+--R | 2
+--R \|x + 1
+--R +
+--R 7 5 3 8
+--R (- 2048x - 4096x - 2432x - 384x)y(x)
+--R +
+--R 8 6 4 2 7
+--R (2048a x + 4096a x + 2432a x + 384a x )y(x)
+--R +
+--R 7 5 3 6
+--R (- 5120x - 10240x - 6080x - 960x)y(x)
+--R +
+--R 8 6 4 2 5
+--R (4096a x + 8192a x + 4864a x + 768a x )y(x)
+--R +
+--R 7 5 3 4
+--R (- 4224x - 8448x - 5016x - 792x)y(x)
+--R +
+--R 8 6 4 2 3
+--R (2432a x + 4864a x + 2888a x + 456a x )y(x)
+--R +
+--R 7 5 3 2
+--R (- 1216x - 2432x - 1444x - 228x)y(x)
+--R +
+--R 8 6 4 2 7 5
3
+--R (384a x + 768a x + 456a x + 72a x )y(x) - 64x - 128x -
76x
+--R +
+--R - 12x
+--R *
+--R ,
+--R y (x)
+--R
+--R +
+--R 6 4 2 7
+--R (2048a x + 3072a x + 1152a x + 64a)y(x)
+--R +
+--R 7 5 3 6
+--R (- 2048x - 4096x - 2432x - 384x)y(x)
+--R +
+--R 6 4 2 5
+--R (3072a x + 4608a x + 1728a x + 96a)y(x)
+--R +
+--R 7 5 3 4
+--R (- 3072x - 6144x - 3648x - 576x)y(x)
+--R +
+--R 6 4 2 3
+--R (1152a x + 1728a x + 648a x + 36a)y(x)
+--R +
+--R 7 5 3 2
+--R (- 1152x - 2304x - 1368x - 216x)y(x)
+--R +
+--R 6 4 2 7 5 3
+--R (64a x + 96a x + 36a x + 2a)y(x) - 64x - 128x - 76x
- 12x
+--R *
+--R +------+
+--R | 2
+--R \|x + 1
+--R +
+--R 7 5 3 7
+--R (- 2048a x - 4096a x - 2432a x - 384a x)y(x)
+--R +
+--R 8 6 4 2 6
+--R (2048x + 5120x + 4224x + 1216x + 64)y(x)
+--R +
+--R 7 5 3 5
+--R (- 3072a x - 6144a x - 3648a x - 576a x)y(x)
+--R +
+--R 8 6 4 2 4
+--R (3072x + 7680x + 6336x + 1824x + 96)y(x)
+--R +
+--R 7 5 3 3
+--R (- 1152a x - 2304a x - 1368a x - 216a x)y(x)
+--R +
+--R 8 6 4 2 2
+--R (1152x + 2880x + 2376x + 684x + 36)y(x)
+--R +
+--R 7 5 3 8 6
4
+--R (- 64a x - 128a x - 76a x - 12a x)y(x) + 64x + 160x +
132x
+--R +
+--R 2
+--R 38x + 2
+--R *
+--R +---------+
+--R | 2
+--R \|y(x) + 1
+--R +
+--R 6 4 2 8
+--R (- 2048a x - 3072a x - 1152a x - 64a)y(x)
+--R +
+--R 7 5 3 7
+--R (2048x + 4096x + 2432x + 384x)y(x)
+--R +
+--R 6 4 2 6
+--R (- 4096a x - 6144a x - 2304a x - 128a)y(x)
+--R +
+--R 7 5 3 5
+--R (4096x + 8192x + 4864x + 768x)y(x)
+--R +
+--R 6 4 2 4
+--R (- 2432a x - 3648a x - 1368a x - 76a)y(x)
+--R +
+--R 7 5 3 3
+--R (2432x + 4864x + 2888x + 456x)y(x)
+--R +
+--R 6 4 2 2
+--R (- 384a x - 576a x - 216a x - 12a)y(x)
+--R +
+--R 7 5 3
+--R (384x + 768x + 456x + 72x)y(x)
+--R *
+--R +------+
+--R | 2
+--R \|x + 1
+--R +
+--R 7 5 3 8
+--R (2048a x + 4096a x + 2432a x + 384a x)y(x)
+--R +
+--R 8 6 4 2 7
+--R (- 2048x - 5120x - 4224x - 1216x - 64)y(x)
+--R +
+--R 7 5 3 6
+--R (4096a x + 8192a x + 4864a x + 768a x)y(x)
+--R +
+--R 8 6 4 2 5
+--R (- 4096x - 10240x - 8448x - 2432x - 128)y(x)
+--R +
+--R 7 5 3 4
+--R (2432a x + 4864a x + 2888a x + 456a x)y(x)
+--R +
+--R 8 6 4 2 3
+--R (- 2432x - 6080x - 5016x - 1444x - 76)y(x)
+--R +
+--R 7 5 3 2
+--R (384a x + 768a x + 456a x + 72a x)y(x)
+--R +
+--R 8 6 4 2
+--R (- 384x - 960x - 792x - 228x - 12)y(x)
+--R *
+--R ROOT
+--R +------+
+--R 3 3 3 | 2
+--R ((64x + 32x)y(x) + (32x + 16x)y(x))\|x + 1
+--R +
+--R 4 2 3 4 2
+--R (- 64x - 64x - 8)y(x) + (- 32x - 32x - 4)y(x)
+--R *
+--R +---------+
+--R | 2
+--R \|y(x) + 1
+--R +
+--R 3 4 3 2 3
+--R ((- 64x - 32x)y(x) + (- 64x - 32x)y(x) - 8x - 4x)
+--R *
+--R +------+
+--R | 2
+--R \|x + 1
+--R +
+--R 4 2 4 4 2 2 4
2
+--R (64x + 64x + 8)y(x) + (64x + 64x + 8)y(x) + 8x +
8x
+--R +
+--R 1
+--R *
+--R +---------+ 2
+--R | 2
+--R log(\|y(x) + 1 - y(x))
+--R +
+--R +------+
+--R 3 3 3 | 2
+--R ((128x + 64x)y(x) + (64x + 32x)y(x))\|x + 1
+--R +
+--R 4 2 3 4 2
+--R (- 128x - 128x - 16)y(x) + (- 64x - 64x -
8)y(x)
+--R *
+--R +------+
+--R | 2
+--R log(\|x + 1 - x)
+--R +
+--R 3 5 4 2 4
+--R (128x + 64x)y(x) + (- 256a x - 128a x )y(x)
+--R +
+--R 5 3 3
+--R (128x + 256x + 80x)y(x)
+--R +
+--R 4 2 2 5 3
+--R (- 128a x - 64a x )y(x) + (64x + 80x +
16x)y(x)
+--R *
+--R +------+
+--R | 2
+--R \|x + 1
+--R +
+--R 4 2 5
+--R (- 128x - 128x - 16)y(x)
+--R +
+--R 5 3 4
+--R (256a x + 256a x + 32a x)y(x)
+--R +
+--R 6 4 2 3
+--R (- 128x - 320x - 192x - 16)y(x)
+--R +
+--R 5 3 2
+--R (128a x + 128a x + 16a x)y(x)
+--R +
+--R 6 4 2
+--R (- 64x - 112x - 48x - 2)y(x)
+--R *
+--R +---------+
+--R | 2
+--R \|y(x) + 1
+--R +
+--R 3 4 3 2
3
+--R (- 128x - 64x)y(x) + (- 128x - 64x)y(x) -
16x
+--R +
+--R - 8x
+--R *
+--R +------+
+--R | 2
+--R \|x + 1
+--R +
+--R 4 2 4 4 2
2
+--R (128x + 128x + 16)y(x) + (128x + 128x + 16)y(x)
+--R +
+--R 4 2
+--R 16x + 16x + 2
+--R *
+--R +------+
+--R | 2
+--R log(\|x + 1 - x)
+--R +
+--R 3 6 4 2 5
+--R (- 128x - 64x)y(x) + (256a x + 128a x )y(x)
+--R +
+--R 5 3 4 4 2
3
+--R (- 128x - 320x - 112x)y(x) + (256a x + 128a x
)y(x)
+--R +
+--R 5 3 2 4 2
+--R (- 128x - 192x - 48x)y(x) + (32a x + 16a x )y(x)
+--R +
+--R 5 3
+--R - 16x - 16x - 2x
+--R *
+--R +------+
+--R | 2
+--R \|x + 1
+--R +
+--R 4 2 6
+--R (128x + 128x + 16)y(x)
+--R +
+--R 5 3 5
+--R (- 256a x - 256a x - 32a x)y(x)
+--R +
+--R 6 4 2 4
+--R (128x + 384x + 256x + 24)y(x)
+--R +
+--R 5 3 3
+--R (- 256a x - 256a x - 32a x)y(x)
+--R +
+--R 6 4 2 2
+--R (128x + 256x + 128x + 8)y(x)
+--R +
+--R 5 3 6 4 2
+--R (- 32a x - 32a x - 4a x)y(x) + 16x + 24x + 8x
+--R *
+--R +---------+
+--R | 2
+--R log(\|y(x) + 1 - y(x))
+--R +
+--R +------+
+--R 3 3 3 | 2
+--R ((64x + 32x)y(x) + (32x + 16x)y(x))\|x + 1
+--R +
+--R 4 2 3 4 2
+--R (- 64x - 64x - 8)y(x) + (- 32x - 32x - 4)y(x)
+--R *
+--R +------+ 2
+--R | 2
+--R log(\|x + 1 - x)
+--R +
+--R 3 5 4 2 4
+--R (128x + 64x)y(x) + (- 256a x - 128a x )y(x)
+--R +
+--R 5 3 3
+--R (128x + 256x + 80x)y(x)
+--R +
+--R 4 2 2 5 3
+--R (- 128a x - 64a x )y(x) + (64x + 80x +
16x)y(x)
+--R *
+--R +------+
+--R | 2
+--R \|x + 1
+--R +
+--R 4 2 5
+--R (- 128x - 128x - 16)y(x)
+--R +
+--R 5 3 4
+--R (256a x + 256a x + 32a x)y(x)
+--R +
+--R 6 4 2 3
+--R (- 128x - 320x - 192x - 16)y(x)
+--R +
+--R 5 3 2
+--R (128a x + 128a x + 16a x)y(x)
+--R +
+--R 6 4 2
+--R (- 64x - 112x - 48x - 2)y(x)
+--R *
+--R +------+
+--R | 2
+--R log(\|x + 1 - x)
+--R +
+--R 3 7 4 2 6
+--R (64x + 32x)y(x) + (- 256a x - 128a x )y(x)
+--R +
+--R 2 5 2 3 5
+--R ((256a + 128)x + (128a + 224)x + 64x)y(x)
+--R +
+--R 6 4 2 4
+--R (- 256a x - 512a x - 160a x )y(x)
+--R +
+--R 7 2 5 2 3
3
+--R (64x + (128a + 224)x + (64a + 448)x + 160x)y(x)
+--R +
+--R 6 4 2 2
+--R (- 128a x - 160a x - 32a x )y(x)
+--R +
+--R 7 5 3
+--R (32x + 64x + 160x + 66x)y(x)
+--R *
+--R +------+
+--R | 2
+--R \|x + 1
+--R +
+--R 4 2 7 5 3
6
+--R (- 64x - 64x - 8)y(x) + (256a x + 256a x + 32a
x)y(x)
+--R +
+--R 2 6 2 4 2
2
+--R (- 256a - 128)x + (- 256a - 288)x + (- 32a -
160)x
+--R +
+--R - 12
+--R *
+--R 5
+--R y(x)
+--R +
+--R 7 5 3 4
+--R (256a x + 640a x + 384a x + 32a x)y(x)
+--R +
+--R 8 2 6 2 4
+--R - 64x + (- 128a - 256)x + (- 128a - 552)x
+--R +
+--R 2 2
+--R (- 16a - 360)x - 36
+--R *
+--R 3
+--R y(x)
+--R +
+--R 7 5 3 2
+--R (128a x + 224a x + 96a x + 4a x)y(x)
+--R +
+--R 8 6 4 2
+--R (- 32x - 80x - 188x - 140x - 16)y(x)
+--R *
+--R +---------+
+--R | 2
+--R \|y(x) + 1
+--R +
+--R 3 4 3 2 3
+--R ((- 64x - 32x)y(x) + (- 64x - 32x)y(x) - 8x - 4x)
+--R *
+--R +------+
+--R | 2
+--R \|x + 1
+--R +
+--R 4 2 4 4 2 2 4
2
+--R (64x + 64x + 8)y(x) + (64x + 64x + 8)y(x) + 8x +
8x
+--R +
+--R 1
+--R *
+--R +------+ 2
+--R | 2
+--R log(\|x + 1 - x)
+--R +
+--R 3 6 4 2 5
+--R (- 128x - 64x)y(x) + (256a x + 128a x )y(x)
+--R +
+--R 5 3 4 4 2
3
+--R (- 128x - 320x - 112x)y(x) + (256a x + 128a x
)y(x)
+--R +
+--R 5 3 2 4 2
+--R (- 128x - 192x - 48x)y(x) + (32a x + 16a x )y(x)
+--R +
+--R 5 3
+--R - 16x - 16x - 2x
+--R *
+--R +------+
+--R | 2
+--R \|x + 1
+--R +
+--R 4 2 6
+--R (128x + 128x + 16)y(x)
+--R +
+--R 5 3 5
+--R (- 256a x - 256a x - 32a x)y(x)
+--R +
+--R 6 4 2 4
+--R (128x + 384x + 256x + 24)y(x)
+--R +
+--R 5 3 3
+--R (- 256a x - 256a x - 32a x)y(x)
+--R +
+--R 6 4 2 2
+--R (128x + 256x + 128x + 8)y(x)
+--R +
+--R 5 3 6 4 2
+--R (- 32a x - 32a x - 4a x)y(x) + 16x + 24x + 8x
+--R *
+--R +------+
+--R | 2
+--R log(\|x + 1 - x)
+--R +
+--R 3 8 4 2 7
+--R (- 64x - 32x)y(x) + (256a x + 128a x )y(x)
+--R +
+--R 2 5 2 3 6
+--R ((- 256a - 128)x + (- 128a - 256)x - 80x)y(x)
+--R +
+--R 6 4 2 5
+--R (256a x + 640a x + 224a x )y(x)
+--R +
+--R 7 2 5 2 3
4
+--R (- 64x + (- 256a - 288)x + (- 128a - 552)x -
188x)y(x)
+--R +
+--R 6 4 2 3
+--R (256a x + 384a x + 96a x )y(x)
+--R +
+--R 7 2 5 2 3
2
+--R (- 64x + (- 32a - 160)x + (- 16a - 360)x -
140x)y(x)
+--R +
+--R 6 4 2 7 5 3
+--R (32a x + 32a x + 4a x )y(x) - 8x - 12x - 36x - 16x
+--R *
+--R +------+
+--R | 2
+--R \|x + 1
+--R +
+--R 4 2 8 5 3 7
+--R (64x + 64x + 8)y(x) + (- 256a x - 256a x - 32a x)y(x)
+--R +
+--R 2 6 2 4 2 2
6
+--R ((256a + 128)x + (256a + 320)x + (32a + 192)x +
16)y(x)
+--R +
+--R 7 5 3 5
+--R (- 256a x - 768a x - 512a x - 48a x)y(x)
+--R +
+--R 8 2 6 2 4 2
2
+--R 64x + (256a + 320)x + (256a + 688)x + (32a +
432)x
+--R +
+--R 41
+--R *
+--R 4
+--R y(x)
+--R +
+--R 7 5 3 3
+--R (- 256a x - 512a x - 256a x - 16a x)y(x)
+--R +
+--R 8 2 6 2 4 2 2
+--R (64x + (32a + 192)x + (32a + 432)x + (4a + 304)x +
33)
+--R *
+--R 2
+--R y(x)
+--R +
+--R 7 5 3 8 6 4 2
+--R (- 32a x - 48a x - 16a x )y(x) + 8x + 16x + 41x + 33x
+ 4
+--R /
+--R +------+
+--R 3 3 3 | 2
+--R ((256x + 128x)y(x) + (128x + 64x)y(x))\|x + 1
+--R +
+--R 4 2 3 4 2
+--R (- 256x - 256x - 32)y(x) + (- 128x - 128x - 16)y(x)
+--R *
+--R +---------+
+--R | 2
+--R \|y(x) + 1
+--R +
+--R 3 4 3 2 3
+--R ((- 256x - 128x)y(x) + (- 256x - 128x)y(x) - 32x -
16x)
+--R *
+--R +------+
+--R | 2
+--R \|x + 1
+--R +
+--R 4 2 4 4 2 2 4
+--R (256x + 256x + 32)y(x) + (256x + 256x + 32)y(x) + 32x
+--R +
+--R 2
+--R 32x + 4
+--R +
+--R 6 4 2 6
+--R (- 1024a x - 1536a x - 576a x - 32a)y(x)
+--R +
+--R 6 4 2 4
+--R (- 1536a x - 2304a x - 864a x - 48a)y(x)
+--R +
+--R 6 4 2 2 6
4
+--R (- 576a x - 864a x - 324a x - 18a)y(x) - 32a x -
48a x
+--R +
+--R 2
+--R - 18a x - a
+--R *
+--R +------+
+--R | 2
+--R \|x + 1
+--R +
+--R 7 5 3 6
+--R (1024a x + 2048a x + 1216a x + 192a x)y(x)
+--R +
+--R 7 5 3 4
+--R (1536a x + 3072a x + 1824a x + 288a x)y(x)
+--R +
+--R 7 5 3 2 7
5
+--R (576a x + 1152a x + 684a x + 108a x)y(x) + 32a x + 64a x
+--R +
+--R 3
+--R 38a x + 6a x
+--R *
+--R +---------+
+--R | 2
+--R \|y(x) + 1
+--R +
+--R 6 4 2 7
+--R (1024a x + 1536a x + 576a x + 32a)y(x)
+--R +
+--R 6 4 2 5
+--R (2048a x + 3072a x + 1152a x + 64a)y(x)
+--R +
+--R 6 4 2 3
+--R (1216a x + 1824a x + 684a x + 38a)y(x)
+--R +
+--R 6 4 2
+--R (192a x + 288a x + 108a x + 6a)y(x)
+--R *
+--R +------+
+--R | 2
+--R \|x + 1
+--R +
+--R 7 5 3 7
+--R (- 1024a x - 2048a x - 1216a x - 192a x)y(x)
+--R +
+--R 7 5 3 5
+--R (- 2048a x - 4096a x - 2432a x - 384a x)y(x)
+--R +
+--R 7 5 3 3
+--R (- 1216a x - 2432a x - 1444a x - 228a x)y(x)
+--R +
+--R 7 5 3
+--R (- 192a x - 384a x - 228a x - 36a x)y(x)
+--R *
+--R +---------+
+--R | 2
+--R log(\|y(x) + 1 - y(x))
+--R +
+--R 7 5 3 7
+--R (- 2048a x - 3072a x - 1152a x - 64a x)y(x)
+--R +
+--R 2 8 2 6 2 4 2 2 6
+--R (2048a x + 3072a x + 1152a x + 64a x )y(x)
+--R +
+--R 7 5 3 5
+--R (- 4096a x - 6144a x - 2304a x - 128a x)y(x)
+--R +
+--R 2 8 2 6 2 4 2 2 4
+--R (3072a x + 4608a x + 1728a x + 96a x )y(x)
+--R +
+--R 7 5 3 3
+--R (- 2432a x - 3648a x - 1368a x - 76a x)y(x)
+--R +
+--R 2 8 2 6 2 4 2 2 2
+--R (1152a x + 1728a x + 648a x + 36a x )y(x)
+--R +
+--R 7 5 3 2 8
2 6
+--R (- 384a x - 576a x - 216a x - 12a x)y(x) + 64a x +
96a x
+--R +
+--R 2 4 2 2
+--R 36a x + 2a x
+--R *
+--R +------+
+--R | 2
+--R \|x + 1
+--R +
+--R 8 6 4 2 7
+--R (2048a x + 4096a x + 2432a x + 384a x )y(x)
+--R +
+--R 2 9 2 7 2 5 2 3 6
+--R (- 2048a x - 4096a x - 2432a x - 384a x )y(x)
+--R +
+--R 8 6 4 2 5
+--R (4096a x + 8192a x + 4864a x + 768a x )y(x)
+--R +
+--R 2 9 2 7 2 5 2 3 4
+--R (- 3072a x - 6144a x - 3648a x - 576a x )y(x)
+--R +
+--R 8 6 4 2 3
+--R (2432a x + 4864a x + 2888a x + 456a x )y(x)
+--R +
+--R 2 9 2 7 2 5 2 3 2
+--R (- 1152a x - 2304a x - 1368a x - 216a x )y(x)
+--R +
+--R 8 6 4 2 2 9 2 7
+--R (384a x + 768a x + 456a x + 72a x )y(x) - 64a x - 128a x
+--R +
+--R 2 5 2 3
+--R - 76a x - 12a x
+--R *
+--R +---------+
+--R | 2
+--R \|y(x) + 1
+--R +
+--R 7 5 3 8
+--R (2048a x + 3072a x + 1152a x + 64a x)y(x)
+--R +
+--R 2 8 2 6 2 4 2 2 7
+--R (- 2048a x - 3072a x - 1152a x - 64a x )y(x)
+--R +
+--R 7 5 3 6
+--R (5120a x + 7680a x + 2880a x + 160a x)y(x)
+--R +
+--R 2 8 2 6 2 4 2 2 5
+--R (- 4096a x - 6144a x - 2304a x - 128a x )y(x)
+--R +
+--R 7 5 3 4
+--R (4224a x + 6336a x + 2376a x + 132a x)y(x)
+--R +
+--R 2 8 2 6 2 4 2 2 3
+--R (- 2432a x - 3648a x - 1368a x - 76a x )y(x)
+--R +
+--R 7 5 3 2
+--R (1216a x + 1824a x + 684a x + 38a x)y(x)
+--R +
+--R 2 8 2 6 2 4 2 2 7
5
+--R (- 384a x - 576a x - 216a x - 12a x )y(x) + 64a x + 96a x
+--R +
+--R 3
+--R 36a x + 2a x
+--R *
+--R +------+
+--R | 2
+--R \|x + 1
+--R +
+--R 8 6 4 2 8
+--R (- 2048a x - 4096a x - 2432a x - 384a x )y(x)
+--R +
+--R 2 9 2 7 2 5 2 3 7
+--R (2048a x + 4096a x + 2432a x + 384a x )y(x)
+--R +
+--R 8 6 4 2 6
+--R (- 5120a x - 10240a x - 6080a x - 960a x )y(x)
+--R +
+--R 2 9 2 7 2 5 2 3 5
+--R (4096a x + 8192a x + 4864a x + 768a x )y(x)
+--R +
+--R 8 6 4 2 4
+--R (- 4224a x - 8448a x - 5016a x - 792a x )y(x)
+--R +
+--R 2 9 2 7 2 5 2 3 3
+--R (2432a x + 4864a x + 2888a x + 456a x )y(x)
+--R +
+--R 8 6 4 2 2
+--R (- 1216a x - 2432a x - 1444a x - 228a x )y(x)
+--R +
+--R 2 9 2 7 2 5 2 3 8 6
+--R (384a x + 768a x + 456a x + 72a x )y(x) - 64a x - 128a x
+--R +
+--R 4 2
+--R - 76a x - 12a x
+--R *
+--R ,
+--R y (x)
+--R
+--R +
+--R 6 4 2 6
+--R (- 1024a x - 1536a x - 576a x - 32a)y(x)
+--R +
+--R 6 4 2 4
+--R (- 1536a x - 2304a x - 864a x - 48a)y(x)
+--R +
+--R 6 4 2 2 6
4
+--R (- 576a x - 864a x - 324a x - 18a)y(x) - 32a x -
48a x
+--R +
+--R 2
+--R - 18a x - a
+--R *
+--R +------+
+--R | 2
+--R \|x + 1
+--R +
+--R 7 5 3 6
+--R (1024a x + 2048a x + 1216a x + 192a x)y(x)
+--R +
+--R 7 5 3 4
+--R (1536a x + 3072a x + 1824a x + 288a x)y(x)
+--R +
+--R 7 5 3 2 7
5
+--R (576a x + 1152a x + 684a x + 108a x)y(x) + 32a x + 64a x
+--R +
+--R 3
+--R 38a x + 6a x
+--R *
+--R +------+
+--R | 2
+--R log(\|x + 1 - x)
+--R +
+--R 6 4 2 8
+--R (- 1024a x - 1536a x - 576a x - 32a)y(x)
+--R +
+--R 2 7 2 5 2 3 2 7
+--R (4096a x + 6144a x + 2304a x + 128a x)y(x)
+--R +
+--R 8 7 6 5 4
3
+--R - 3072a x - 2048x - 8192a x - 4096x - 6720a x -
2432x
+--R +
+--R 2
+--R - 1728a x - 384x - 64a
+--R *
+--R 6
+--R y(x)
+--R +
+--R 2 7 2 5 2 3 2 5
+--R (6144a x + 9216a x + 3456a x + 192a x)y(x)
+--R +
+--R 8 7 6 5 4
3
+--R - 4608a x - 3072x - 10432a x - 6144x - 7296a x -
3648x
+--R +
+--R 2
+--R - 1548a x - 576x - 38a
+--R *
+--R 4
+--R y(x)
+--R +
+--R 2 7 2 5 2 3 2 3
+--R (2304a x + 3456a x + 1296a x + 72a x)y(x)
+--R +
+--R 8 7 6 5 4
3
+--R - 1728a x - 1152x - 3648a x - 2304x - 2340a x -
1368x
+--R +
+--R 2
+--R - 432a x - 216x - 6a
+--R *
+--R 2
+--R y(x)
+--R +
+--R 2 7 2 5 2 3 2 8 7
6
+--R (128a x + 192a x + 72a x + 4a x)y(x) - 96a x - 64x -
192a x
+--R +
+--R 5 4 3 2
+--R - 128x - 114a x - 76x - 18a x - 12x
+--R *
+--R +------+
+--R | 2
+--R \|x + 1
+--R +
+--R 7 5 3 8
+--R (1024a x + 2048a x + 1216a x + 192a x)y(x)
+--R +
+--R 2 8 2 6 2 4 2 2 7
+--R (- 4096a x - 8192a x - 4864a x - 768a x )y(x)
+--R +
+--R 9 8 7 6 5 4
+--R 3072a x + 2048x + 9728a x + 5120x + 10432a x + 4224x
+--R +
+--R 3 2
+--R 4256a x + 1216x + 480a x + 64
+--R *
+--R 6
+--R y(x)
+--R +
+--R 2 8 2 6 2 4 2 2 5
+--R (- 6144a x - 12288a x - 7296a x - 1152a x )y(x)
+--R +
+--R 9 8 7 6 5 4
+--R 4608a x + 3072x + 12736a x + 7680x + 11936a x + 6336x
+--R +
+--R 3 2
+--R 4180a x + 1824x + 372a x + 96
+--R *
+--R 4
+--R y(x)
+--R +
+--R 2 8 2 6 2 4 2 2 3
+--R (- 2304a x - 4608a x - 2736a x - 432a x )y(x)
+--R +
+--R 9 8 7 6 5 4
+--R 1728a x + 1152x + 4512a x + 2880x + 3948a x + 2376x
+--R +
+--R 3 2
+--R 1254a x + 684x + 90a x + 36
+--R *
+--R 2
+--R y(x)
+--R +
+--R 2 8 2 6 2 4 2 2 9 8
+--R (- 128a x - 256a x - 152a x - 24a x )y(x) + 96a x + 64x
+--R +
+--R 7 6 5 4 3 2
+--R 240a x + 160x + 198a x + 132x + 57a x + 38x + 3a x + 2
+--R *
+--R +---------+
+--R | 2
+--R \|y(x) + 1
+--R +
+--R 6 4 2 7
+--R (1024a x + 1536a x + 576a x + 32a)y(x)
+--R +
+--R 6 4 2 5
+--R (2048a x + 3072a x + 1152a x + 64a)y(x)
+--R +
+--R 6 4 2 3
+--R (1216a x + 1824a x + 684a x + 38a)y(x)
+--R +
+--R 6 4 2
+--R (192a x + 288a x + 108a x + 6a)y(x)
+--R *
+--R +------+
+--R | 2
+--R \|x + 1
+--R +
+--R 7 5 3 7
+--R (- 1024a x - 2048a x - 1216a x - 192a x)y(x)
+--R +
+--R 7 5 3 5
+--R (- 2048a x - 4096a x - 2432a x - 384a x)y(x)
+--R +
+--R 7 5 3 3
+--R (- 1216a x - 2432a x - 1444a x - 228a x)y(x)
+--R +
+--R 7 5 3
+--R (- 192a x - 384a x - 228a x - 36a x)y(x)
+--R *
+--R +------+
+--R | 2
+--R log(\|x + 1 - x)
+--R +
+--R 6 4 2 9
+--R (1024a x + 1536a x + 576a x + 32a)y(x)
+--R +
+--R 2 7 2 5 2 3 2 8
+--R (- 4096a x - 6144a x - 2304a x - 128a x)y(x)
+--R +
+--R 8 7 6 5 4 3
+--R 3072a x + 2048x + 8704a x + 4096x + 7488a x + 2432x
+--R +
+--R 2
+--R 2016a x + 384x + 80a
+--R *
+--R 7
+--R y(x)
+--R +
+--R 2 7 2 5 2 3 2 6
+--R (- 8192a x - 12288a x - 4608a x - 256a x)y(x)
+--R +
+--R 8 7 6 5 4 3
+--R 6144a x + 4096x + 14400a x + 8192x + 10464a x + 4864x
+--R +
+--R 2
+--R 2340a x + 768x + 66a
+--R *
+--R 5
+--R y(x)
+--R +
+--R 2 7 2 5 2 3 2 4
+--R (- 4864a x - 7296a x - 2736a x - 152a x)y(x)
+--R +
+--R 8 7 6 5 4 3
+--R 3648a x + 2432x + 7904a x + 4864x + 5244a x + 2888x
+--R +
+--R 2
+--R 1026a x + 456x + 19a
+--R *
+--R 3
+--R y(x)
+--R +
+--R 2 7 2 5 2 3 2 2
+--R (- 768a x - 1152a x - 432a x - 24a x)y(x)
+--R +
+--R 8 7 6 5 4 3
2
+--R 576a x + 384x + 1184a x + 768x + 732a x + 456x + 126a x
+--R +
+--R 72x + a
+--R *
+--R y(x)
+--R *
+--R +------+
+--R | 2
+--R \|x + 1
+--R +
+--R 7 5 3 9
+--R (- 1024a x - 2048a x - 1216a x - 192a x)y(x)
+--R +
+--R 2 8 2 6 2 4 2 2 8
+--R (4096a x + 8192a x + 4864a x + 768a x )y(x)
+--R +
+--R 9 8 7 6 5 4
+--R - 3072a x - 2048x - 10240a x - 5120x - 11456a x - 4224x
+--R +
+--R 3 2
+--R - 4864a x - 1216x - 576a x - 64
+--R *
+--R 7
+--R y(x)
+--R +
+--R 2 8 2 6 2 4 2 2 6
+--R (8192a x + 16384a x + 9728a x + 1536a x )y(x)
+--R +
+--R 9 8 7 6 5 4
+--R - 6144a x - 4096x - 17472a x - 10240x - 16896a x - 8448x
+--R +
+--R 3 2
+--R - 6156a x - 2432x - 588a x - 128
+--R *
+--R 5
+--R y(x)
+--R +
+--R 2 8 2 6 2 4 2 2 4
+--R (4864a x + 9728a x + 5776a x + 912a x )y(x)
+--R +
+--R 9 8 7 6 5 4
+--R - 3648a x - 2432x - 9728a x - 6080x - 8740a x - 5016x
+--R +
+--R 3 2
+--R - 2888a x - 1444x - 228a x - 76
+--R *
+--R 3
+--R y(x)
+--R +
+--R 2 8 2 6 2 4 2 2 2
+--R (768a x + 1536a x + 912a x + 144a x )y(x)
+--R +
+--R 9 8 7 6 5 4 3
+--R - 576a x - 384x - 1472a x - 960x - 1252a x - 792x - 380a x
+--R +
+--R 2
+--R - 228x - 24a x - 12
+--R *
+--R y(x)
+--R /
+--R 6 4 2 6
+--R (2048x + 3072x + 1152x + 64)y(x)
+--R +
+--R 6 4 2 4
+--R (3072x + 4608x + 1728x + 96)y(x)
+--R +
+--R 6 4 2 2 6 4 2
+--R (1152x + 1728x + 648x + 36)y(x) + 64x + 96x + 36x + 2
+--R *
+--R +------+
+--R | 2
+--R \|x + 1
+--R +
+--R 7 5 3 6
+--R (- 2048x - 4096x - 2432x - 384x)y(x)
+--R +
+--R 7 5 3 4
+--R (- 3072x - 6144x - 3648x - 576x)y(x)
+--R +
+--R 7 5 3 2 7 5 3
+--R (- 1152x - 2304x - 1368x - 216x)y(x) - 64x - 128x - 76x -
12x
+--R *
+--R +---------+
+--R | 2
+--R \|y(x) + 1
+--R +
+--R 6 4 2 7
+--R (- 2048x - 3072x - 1152x - 64)y(x)
+--R +
+--R 6 4 2 5
+--R (- 4096x - 6144x - 2304x - 128)y(x)
+--R +
+--R 6 4 2 3
+--R (- 2432x - 3648x - 1368x - 76)y(x)
+--R +
+--R 6 4 2
+--R (- 384x - 576x - 216x - 12)y(x)
+--R *
+--R +------+
+--R | 2
+--R \|x + 1
+--R +
+--R 7 5 3 7
+--R (2048x + 4096x + 2432x + 384x)y(x)
+--R +
+--R 7 5 3 5
+--R (4096x + 8192x + 4864x + 768x)y(x)
+--R +
+--R 7 5 3 3 7 5 3
+--R (2432x + 4864x + 2888x + 456x)y(x) + (384x + 768x + 456x +
72x)y(x)
+--R Type: Expression
Integer
+--E 85
+
+--S 86 of 120
+--Rode337 := (sqrt(y(x)**2+x**2)+x)*D(y(x),x)-y(x)
+--R
+--R
+--R +----------+
+--R | 2 2 ,
+--R (85) (\|y(x) + x + x)y (x) - y(x)
+--R
+--R Type: Expression
Integer
+--E 86
+
+--S 87 of 120
+--Rsolve(ode337,y,x)
+--R
+--R
+--R (86) "failed"
+--R Type:
Union("failed",...)
+--E 87
+
+--S 88 of 120
+--Rode338 := (y(x)*sqrt(y(x)**2+x**2)+(y(x)**2-x**2)*sin(alpha)-_
+--R 2*x*y(x)*cos(alpha))*D(y(x),x)+x*sqrt(y(x)**2+x**2)+_
+--R 2*x*y(x)*sin(alpha)+(y(x)**2-x**2)*cos(alpha)
+--R
+--R
+--R (87)
+--R +----------+
+--R | 2 2 2 2 ,
+--R (y(x)\|y(x) + x + (y(x) - x )sin(alpha) - 2x y(x)cos(alpha))y (x)
+--R
+--R +
+--R +----------+
+--R | 2 2 2 2
+--R x\|y(x) + x + 2x y(x)sin(alpha) + (y(x) - x )cos(alpha)
+--R Type: Expression
Integer
+--E 88
+
+--S 89 of 120
+--Rsolve(ode338,y,x)
+--R
+--R
+--R (88) "failed"
+--R Type:
Union("failed",...)
+--E 89
+
+--S 90 of 120
+--Rode339 := (x*sqrt(x**2+y(x)**2+1)-y(x)*(x**2+y(x)**2))*D(y(x),x)-_
+--R y(x)*sqrt(x**2+y(x)**2+1)-x*(x**2+y(x)**2)
+--R
+--R
+--R (89)
+--R +--------------+ +--------------+
+--R | 2 2 3 2 , | 2 2
+--R (x\|y(x) + x + 1 - y(x) - x y(x))y (x) - y(x)\|y(x) + x + 1
+--R
+--R +
+--R 2 3
+--R - x y(x) - x
+--R Type: Expression
Integer
+--E 90
+
+--S 91 of 120
+--Rsolve(ode339,y,x)
+--R
+--R
+--R (90) "failed"
+--R Type:
Union("failed",...)
+--E 91
+
+--S 92 of 120
+--Rode340 := (e1*(x+a)/((x+a)**2+y(x)**2)**(3/2)+e2*(x-a)/_
+--R ((x-a)**2+y(x)**2)**(3/2))*D(y(x),x)-y(x)*_
+--R (e1/((x+a)**2+y(x)**2)**(3/2)+e2/((x-a)**2+y(x)**2)**(3/2))
+--R
+--R
+--R (91)
+--R 2 3 2 2 3
+--R ((e2 x - a e2)y(x) + e2 x + a e2 x - a e2 x - a e2)
+--R *
+--R +----------------------+
+--R | 2 2 2
+--R \|y(x) + x + 2a x + a
+--R +
+--R 2 3 2 2 3
+--R ((e1 x + a e1)y(x) + e1 x - a e1 x - a e1 x + a e1)
+--R *
+--R +----------------------+
+--R | 2 2 2
+--R \|y(x) + x - 2a x + a
+--R *
+--R ,
+--R y (x)
+--R
+--R +
+--R
+----------------------+
+--R 3 2 2 | 2 2 2
+--R (- e2 y(x) + (- e2 x - 2a e2 x - a e2)y(x))\|y(x) + x + 2a x + a
+--R +
+--R
+----------------------+
+--R 3 2 2 | 2 2 2
+--R (- e1 y(x) + (- e1 x + 2a e1 x - a e1)y(x))\|y(x) + x - 2a x + a
+--R /
+--R +----------------------+
+--R 4 2 2 2 4 2 2 4 | 2 2 2
+--R (y(x) + (2x + 2a )y(x) + x - 2a x + a )\|y(x) + x - 2a x + a
+--R *
+--R +----------------------+
+--R | 2 2 2
+--R \|y(x) + x + 2a x + a
+--R Type: Expression
Integer
+--E 92
+
+--S 93 of 120
+--Rsolve(ode340,y,x)
+--R
+--R
+--R (92) "failed"
+--R Type:
Union("failed",...)
+--E 93
+
+--S 94 of 120
+--Rode341 := (x*exp(y(x))+exp(x))*D(y(x),x)+exp(y(x))+y(x)*exp(x)
+--R
+--R
+--R y(x) x , y(x) x
+--R (93) (x %e + %e )y (x) + %e + y(x)%e
+--R
+--R Type: Expression
Integer
+--E 94
+
+--S 95 of 120
+--Ryx:=solve(ode341,y,x)
+--R
+--R
+--R y(x) x
+--R (94) x %e + y(x)%e
+--R Type: Union(Expression
Integer,...)
+--E 95
+
+--S 96 of 120
+--Rode341expr := (x*exp(yx)+exp(x))*D(yx,x)+exp(yx)+yx*exp(x)
+--R
+--R
+--R (95)
+--R y(x)
x
+--R 2 y(x) x , y(x) x x %e + y(x)%e
+--R ((x %e + x %e )y (x) + x %e + x y(x)%e + 1)%e
+--R
+--R +
+--R x y(x) x 2 , x y(x) x 2
+--R (x %e %e + (%e ) )y (x) + (x + 1)%e %e + 2y(x)(%e )
+--R
+--R Type: Expression
Integer
+--E 96
+
+--S 97 of 120
+--Rode342 := x*(3*exp(x*y(x))+2*exp(-x*y(x)))*(x*D(y(x),x)+y(x))+1
+--R
+--R
+--R (96)
+--R 2 x y(x) 2 - x y(x) , x y(x) - x y(x)
+--R (3x %e + 2x %e )y (x) + 3x y(x)%e + 2x y(x)%e
+ 1
+--R
+--R Type: Expression
Integer
+--E 97
+
+--S 98 of 120
+--Ryx:=solve(ode342,y,x)
+--R
+--R
+--R x y(x) 2 x y(x)
+--R 3(%e ) + log(x)%e - 2
+--R (97) ---------------------------------
+--R x y(x)
+--R %e
+--R Type: Union(Expression
Integer,...)
+--E 98
+
+--S 99 of 120
+--Rode342expr := x*(3*exp(x*yx)+2*exp(-x*yx))*(x*D(yx,x)+yx)+1
+--R
+--R
+--R (98)
+--R 3 x y(x) 2 3 , 2 x y(x) 2
+--R (9x (%e ) + 6x )y (x) + (9x y(x) + 9x)(%e )
+--R
+--R +
+--R x y(x) 2
+--R (3x log(x) + 3x)%e + 6x y(x) - 6x
+--R *
+--R x y(x) 2 x y(x)
+--R 3x (%e ) + x log(x)%e - 2x
+--R --------------------------------------
+--R x y(x)
+--R %e
+--R %e
+--R +
+--R 3 x y(x) 2 3 , 2 x y(x) 2
+--R (6x (%e ) + 4x )y (x) + (6x y(x) + 6x)(%e )
+--R
+--R +
+--R x y(x) 2
+--R (2x log(x) + 2x)%e + 4x y(x) - 4x
+--R *
+--R x y(x) 2 x y(x)
+--R - 3x (%e ) - x log(x)%e + 2x
+--R ----------------------------------------
+--R x y(x)
+--R %e
+--R %e
+--R +
+--R x y(x)
+--R %e
+--R /
+--R x y(x)
+--R %e
+--R Type: Expression
Integer
+--E 99
+
+--S 100 of 120
+--Rode343 := (log(y(x))+x)*D(y(x),x)-1
+--R
+--R
+--R ,
+--R (99) (log(y(x)) + x)y (x) - 1
+--R
+--R Type: Expression
Integer
+--E 100
+
+--S 101 of 120
+--Ryx:=solve(ode343,y,x)
+--R
+--R
+--R - y(x) - y(x)
+--R (100) - %e log(y(x)) - x %e + Ei(- y(x))
+--R Type: Union(Expression
Integer,...)
+--E 101
+
+--S 102 of 120
+--Rode343expr := (log(yx)+x)*D(yx,x)-1
+--R
+--R
+--R (101)
+--R - y(x) - y(x) , - y(x)
+--R ((%e log(y(x)) + x %e )y (x) - %e )
+--R
+--R *
+--R - y(x) - y(x)
+--R log(- %e log(y(x)) - x %e + Ei(- y(x)))
+--R +
+--R - y(x) 2 - y(x) , - y(x)
+--R (x %e log(y(x)) + x %e )y (x) - x %e - 1
+--R
+--R Type: Expression
Integer
+--E 102
+
+--S 103 of 120
+--Rode344 := (log(y(x))+2*x-1)*D(y(x),x)-2*y(x)
+--R
+--R
+--R ,
+--R (102) (log(y(x)) + 2x - 1)y (x) - 2y(x)
+--R
+--R Type: Expression
Integer
+--E 103
+
+--S 104 of 120
+--Ryx:=solve(ode344,y,x)
+--R
+--R
+--R - log(y(x)) - 2x
+--R (103) ----------------
+--R y(x)
+--R Type: Union(Expression
Integer,...)
+--E 104
+
+--S 105 of 120
+--Rode344expr := (log(yx)+2*x-1)*D(yx,x)-2*yx
+--R
+--R
+--R (104)
+--R , - log(y(x)) - 2x
+--R ((log(y(x)) + 2x - 1)y (x) - 2y(x))log(----------------)
+--R y(x)
+--R +
+--R 2 ,
+--R ((2x - 1)log(y(x)) + 4x - 4x + 1)y (x) + 2y(x)log(y(x)) + 2y(x)
+--R
+--R /
+--R 2
+--R y(x)
+--R Type: Expression
Integer
+--E 105
+
+--S 106 of 120
+--Rode345 := x*(2*x**2*y(x)*log(y(x))+1)*D(y(x),x)-2*y(x)
+--R
+--R
+--R 3 ,
+--R (105) (2x y(x)log(y(x)) + x)y (x) - 2y(x)
+--R
+--R Type: Expression
Integer
+--E 106
+
+--S 107 of 120
+--Ryx:=solve(ode345,y,x)
+--R
+--R
+--R 2 2 2 2
+--R 2x y(x) log(y(x)) - x y(x) + 2y(x)
+--R (106) -----------------------------------
+--R 2
+--R 2x
+--R Type: Union(Expression
Integer,...)
+--E 107
+
+--S 108 of 120
+--Rode345expr := x*(2*x**2*yx*log(yx)+1)*D(yx,x)-2*yx
+--R
+--R
+--R (107)
+--R 5 3 2 5 3 3 2 3
2
+--R 4x y(x) log(y(x)) + (- 2x y(x) + 6x y(x) )log(y(x)) - x
y(x)
+--R +
+--R 2x y(x)
+--R *
+--R ,
+--R y (x)
+--R
+--R +
+--R 2 3 2 3 2
+--R - 4x y(x) log(y(x)) + 2x y(x) - 4y(x)
+--R *
+--R 2 2 2 2
+--R 2x y(x) log(y(x)) - x y(x) + 2y(x)
+--R log(-----------------------------------)
+--R 2
+--R 2x
+--R +
+--R 3 , 2 2 2 2
+--R (2x y(x)log(y(x)) + x)y (x) - 2x y(x) log(y(x)) + x y(x) - 4y(x)
+--R
+--R /
+--R 2
+--R x
+--R Type: Expression
Integer
+--E 108
+
+--S 109 of 120
+--Rode346 := x*(y(x)*log(x*y(x))+y(x)-a*x)*D(y(x),x)-_
+--R y(x)*(a*x*log(x*y(x))-y(x)+a*x)
+--R
+--R
+--R (108)
+--R 2 , 2
+--R (x y(x)log(x y(x)) + x y(x) - a x )y (x) - a x y(x)log(x y(x)) + y(x)
+--R
+--R +
+--R - a x y(x)
+--R Type: Expression
Integer
+--E 109
+
+--S 110 of 120
+--Rsolve(ode346,y,x)
+--R
+--R
+--R (109) "failed"
+--R Type:
Union("failed",...)
+--E 110
+
+--S 111 of 120
+--Rode347 := D(y(x),x)*(1+sin(x))*sin(y(x))+cos(x)*(cos(y(x))-1)
+--R
+--R
+--R ,
+--R (110) (sin(x) + 1)sin(y(x))y (x) + cos(x)cos(y(x)) - cos(x)
+--R
+--R Type: Expression
Integer
+--E 111
+
+--S 112 of 120
+--Ryx:=solve(ode347,y,x)
+--R
+--R
+--R (111)
+--R 2 2 2
+--R (- 4cos(x) - 8cos(x) - 4)sin(x) + (- 8cos(x) - 16cos(x) -
8)sin(x)
+--R +
+--R 2
+--R - 4cos(x) - 8cos(x) - 4
+--R *
+--R cos(y(x))
+--R +
+--R 5 4 2
3
+--R - sin(x) + (- 4cos(x) - 4)sin(x) + (- 6cos(x) - 12cos(x) -
6)sin(x)
+--R +
+--R 3 2 2
+--R (- 4cos(x) - 12cos(x) - 12cos(x) - 4)sin(x)
+--R +
+--R 4 3 2
+--R (- cos(x) - 4cos(x) - 6cos(x) - 4cos(x) - 1)sin(x)
+--R /
+--R 5 4 2 3
+--R sin(x) + (4cos(x) + 5)sin(x) + (6cos(x) + 16cos(x) + 10)sin(x)
+--R +
+--R 3 2 2
+--R (4cos(x) + 18cos(x) + 24cos(x) + 10)sin(x)
+--R +
+--R 4 3 2 4
+--R (cos(x) + 8cos(x) + 18cos(x) + 16cos(x) + 5)sin(x) + cos(x)
+--R +
+--R 3 2
+--R 4cos(x) + 6cos(x) + 4cos(x) + 1
+--R Type: Union(Expression
Integer,...)
+--E 112
+
+--S 113 of 120
+--Rode347expr := D(yx,x)*(1+sin(x))*sin(yx)+cos(x)*(cos(yx)-1)
+--R
+--R
+--R (112)
+--R 2 4
+--R (- 4cos(x) - 8cos(x) - 4)sin(x)
+--R +
+--R 3 2 3
+--R (- 4cos(x) - 24cos(x) - 36cos(x) - 16)sin(x)
+--R +
+--R 3 2 2
+--R (- 12cos(x) - 48cos(x) - 60cos(x) - 24)sin(x)
+--R +
+--R 3 2 3
+--R (- 12cos(x) - 40cos(x) - 44cos(x) - 16)sin(x) - 4cos(x)
+--R +
+--R 2
+--R - 12cos(x) - 12cos(x) - 4
+--R *
+--R ,
+--R sin(y(x))y (x)
+--R
+--R +
+--R 5 2 4
+--R (- 8cos(x) - 8)sin(x) + (8cos(x) - 8cos(x) - 16)sin(x)
+--R +
+--R 3 3
+--R (- 12cos(x) + 12cos(x))sin(x)
+--R +
+--R 4 3 2 2
+--R (4cos(x) - 28cos(x) - 44cos(x) + 4cos(x) + 16)sin(x)
+--R +
+--R 4 3 2
+--R (8cos(x) - 20cos(x) - 56cos(x) - 20cos(x) + 8)sin(x)
+--R +
+--R 4 3 2
+--R 4cos(x) - 4cos(x) - 20cos(x) - 12cos(x)
+--R *
+--R cos(y(x))
+--R +
+--R 5 2 4
+--R cos(x)sin(x) + (5cos(x) + 5cos(x))sin(x)
+--R +
+--R 3 2 3
+--R (10cos(x) + 20cos(x) + 10cos(x))sin(x)
+--R +
+--R 4 3 2 2
+--R (10cos(x) + 30cos(x) + 30cos(x) + 10cos(x))sin(x)
+--R +
+--R 5 4 3 2
+--R (5cos(x) + 20cos(x) + 30cos(x) + 20cos(x) + 5cos(x))sin(x)
+--R +
+--R 6 5 4 3 2
+--R cos(x) + 5cos(x) + 10cos(x) + 10cos(x) + 5cos(x) + cos(x)
+--R *
+--R sin
+--R 2 2
+--R (4cos(x) + 8cos(x) + 4)sin(x)
+--R +
+--R 2 2
+--R (8cos(x) + 16cos(x) + 8)sin(x) + 4cos(x) + 8cos(x) + 4
+--R *
+--R cos(y(x))
+--R +
+--R 5 4
+--R sin(x) + (4cos(x) + 4)sin(x)
+--R +
+--R 2 3
+--R (6cos(x) + 12cos(x) + 6)sin(x)
+--R +
+--R 3 2 2
+--R (4cos(x) + 12cos(x) + 12cos(x) + 4)sin(x)
+--R +
+--R 4 3 2
+--R (cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1)sin(x)
+--R /
+--R 5 4
+--R sin(x) + (4cos(x) + 5)sin(x)
+--R +
+--R 2 3
+--R (6cos(x) + 16cos(x) + 10)sin(x)
+--R +
+--R 3 2 2
+--R (4cos(x) + 18cos(x) + 24cos(x) + 10)sin(x)
+--R +
+--R 4 3 2
4
+--R (cos(x) + 8cos(x) + 18cos(x) + 16cos(x) + 5)sin(x) +
cos(x)
+--R +
+--R 3 2
+--R 4cos(x) + 6cos(x) + 4cos(x) + 1
+--R +
+--R 6 2 5
+--R cos(x)sin(x) + (5cos(x) + 6cos(x))sin(x)
+--R +
+--R 3 2 4
+--R (10cos(x) + 25cos(x) + 15cos(x))sin(x)
+--R +
+--R 4 3 2 3
+--R (10cos(x) + 40cos(x) + 50cos(x) + 20cos(x))sin(x)
+--R +
+--R 5 4 3 2 2
+--R (5cos(x) + 30cos(x) + 60cos(x) + 50cos(x) + 15cos(x))sin(x)
+--R +
+--R 6 5 4 3 2
+--R (cos(x) + 10cos(x) + 30cos(x) + 40cos(x) + 25cos(x) +
6cos(x))
+--R *
+--R sin(x)
+--R +
+--R 6 5 4 3 2
+--R cos(x) + 5cos(x) + 10cos(x) + 10cos(x) + 5cos(x) + cos(x)
+--R *
+--R cos
+--R 2 2
+--R (4cos(x) + 8cos(x) + 4)sin(x)
+--R +
+--R 2 2
+--R (8cos(x) + 16cos(x) + 8)sin(x) + 4cos(x) + 8cos(x) + 4
+--R *
+--R cos(y(x))
+--R +
+--R 5 4
+--R sin(x) + (4cos(x) + 4)sin(x)
+--R +
+--R 2 3
+--R (6cos(x) + 12cos(x) + 6)sin(x)
+--R +
+--R 3 2 2
+--R (4cos(x) + 12cos(x) + 12cos(x) + 4)sin(x)
+--R +
+--R 4 3 2
+--R (cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1)sin(x)
+--R /
+--R 5 4
+--R sin(x) + (4cos(x) + 5)sin(x)
+--R +
+--R 2 3
+--R (6cos(x) + 16cos(x) + 10)sin(x)
+--R +
+--R 3 2 2
+--R (4cos(x) + 18cos(x) + 24cos(x) + 10)sin(x)
+--R +
+--R 4 3 2
4
+--R (cos(x) + 8cos(x) + 18cos(x) + 16cos(x) + 5)sin(x) +
cos(x)
+--R +
+--R 3 2
+--R 4cos(x) + 6cos(x) + 4cos(x) + 1
+--R +
+--R 6 2 5
+--R - cos(x)sin(x) + (- 5cos(x) - 6cos(x))sin(x)
+--R +
+--R 3 2 4
+--R (- 10cos(x) - 25cos(x) - 15cos(x))sin(x)
+--R +
+--R 4 3 2 3
+--R (- 10cos(x) - 40cos(x) - 50cos(x) - 20cos(x))sin(x)
+--R +
+--R 5 4 3 2 2
+--R (- 5cos(x) - 30cos(x) - 60cos(x) - 50cos(x) - 15cos(x))sin(x)
+--R +
+--R 6 5 4 3 2
+--R (- cos(x) - 10cos(x) - 30cos(x) - 40cos(x) - 25cos(x) -
6cos(x))
+--R *
+--R sin(x)
+--R +
+--R 6 5 4 3 2
+--R - cos(x) - 5cos(x) - 10cos(x) - 10cos(x) - 5cos(x) - cos(x)
+--R /
+--R 6 5 2 4
+--R sin(x) + (5cos(x) + 6)sin(x) + (10cos(x) + 25cos(x) + 15)sin(x)
+--R +
+--R 3 2 3
+--R (10cos(x) + 40cos(x) + 50cos(x) + 20)sin(x)
+--R +
+--R 4 3 2 2
+--R (5cos(x) + 30cos(x) + 60cos(x) + 50cos(x) + 15)sin(x)
+--R +
+--R 5 4 3 2
+--R (cos(x) + 10cos(x) + 30cos(x) + 40cos(x) + 25cos(x) + 6)sin(x)
+--R +
+--R 5 4 3 2
+--R cos(x) + 5cos(x) + 10cos(x) + 10cos(x) + 5cos(x) + 1
+--R Type: Expression
Integer
+--E 113
+
+--S 114 of 120
+--Rode348 := (x*cos(y(x))+sin(x))*D(y(x),x)+y(x)*cos(x)+sin(y(x))
+--R
+--R
+--R ,
+--R (113) (x cos(y(x)) + sin(x))y (x) + sin(y(x)) + y(x)cos(x)
+--R
+--R Type: Expression
Integer
+--E 114
+
+--S 115 of 120
+--Ryx:=solve(ode348,y,x)
+--R
+--R
+--R (114) x sin(y(x)) + y(x)sin(x)
+--R Type: Union(Expression
Integer,...)
+--E 115
+
+--S 116 of 120
+--Rode348expr := (x*cos(yx)+sin(x))*D(yx,x)+yx*cos(x)+sin(yx)
+--R
+--R
+--R (115)
+--R sin(x sin(y(x)) + y(x)sin(x))
+--R +
+--R 2 ,
+--R ((x cos(y(x)) + x sin(x))y (x) + x sin(y(x)) + x y(x)cos(x))
+--R
+--R *
+--R cos(x sin(y(x)) + y(x)sin(x))
+--R +
+--R 2 ,
+--R (x sin(x)cos(y(x)) + sin(x) )y (x) + (sin(x) + x cos(x))sin(y(x))
+--R
+--R +
+--R 2y(x)cos(x)sin(x)
+--R Type: Expression
Integer
+--E 116
+
+--S 117 of 120
+--Rode349 := x*D(y(x),x)*cot(y(x)/x)+2*x*sin(y(x)/x)-y(x)*cot(y(x)/x)
+--R
+--R
+--R y(x) , y(x) y(x)
+--R (116) x cot(----)y (x) + 2x sin(----) - y(x)cot(----)
+--R x x x
+--R Type: Expression
Integer
+--E 117
+
+--S 118 of 120
+--Rsolve(ode349,y,x)
+--R
+--R
+--R (117) "failed"
+--R Type:
Union("failed",...)
+--E 118
+
+--S 119 of 120
+--Rode350 := D(y(x),x)*cos(y(x))-cos(x)*sin(y(x))**2-sin(y(x))
+--R
+--R
+--R , 2
+--R (118) cos(y(x))y (x) - cos(x)sin(y(x)) - sin(y(x))
+--R
+--R Type: Expression
Integer
+--E 119
+
+--S 120 of 120
+--Rsolve(ode350,y,x)
+--R
+--R
+--R (119) "failed"
+--R Type:
Union("failed",...)
+--E 120
+
+
+)spool
+)lisp (bye)
+
+@
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} {\bf http://www.cs.uwaterloo.ca/$\tilde{}$ecterrab/odetools.html}
+\end{thebibliography}
+\end{document}
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