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[Axiom-developer] 20071004.02.tpd.patch
|
From: |
daly |
|
Subject: |
[Axiom-developer] 20071004.02.tpd.patch |
|
Date: |
Thu, 4 Oct 2007 16:19:05 -0500 |
This patch adds the next 50 Kamke ordinary differential equations in
Axiom syntax as a regression test.
=======================================================================
diff --git a/changelog b/changelog
index 46dc9dc..44f04bc 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,5 @@
+20071004 tpd src/input/Makefile kamke1.input regression test added
+20071004 tpd src/input/kamke1.input ODE regression test added
20071004 tpd src/input/Makefile kamke0.input regression test added
20071004 tpd src/input/kamke0.input ODE regression test added
20071001 tpd src/algebra/exposed.lisp add (|AxiomServer| . AXSERV) to basic
diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet
index c1ade3e..159377a 100644
--- a/src/input/Makefile.pamphlet
+++ b/src/input/Makefile.pamphlet
@@ -322,7 +322,7 @@ REGRES= algaggr.regress algbrbf.regress algfacob.regress
alist.regress \
intmix2.regress intmix.regress int.regress intrf.regress \
iprntpk.regress \
ipftest.regress is.regress isprime.regress kafile.regress \
- kamke0.regress \
+ kamke0.regress kamke1.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 \
@@ -561,7 +561,7 @@ FILES= ${OUT}/algaggr.input ${OUT}/algbrbf.input
${OUT}/algfacob.input \
${OUT}/intg0.input ${OUT}/intheory.input ${OUT}/int.input \
${OUT}/intlf.input ${OUT}/intmix.input ${OUT}/intrf.input \
${OUT}/ipftest.input ${OUT}/is.input ${OUT}/isprime.input \
- ${OUT}/kafile.input ${OUT}/kamke0.input \
+ ${OUT}/kafile.input ${OUT}/kamke0.input ${OUT}/kamke1.input \
${OUT}/kernel.input ${OUT}/knot.input \
${OUT}/kovacic.input ${OUT}/kuipers.input \
${OUT}/laplace.input ${OUT}/leg.input ${OUT}/lexp.input \
@@ -827,7 +827,7 @@ DOCFILES= \
${DOC}/intmix.input.dvi ${DOC}/intrf.input.dvi \
${DOC}/ipftest.input.dvi ${DOC}/is.input.dvi \
${DOC}/isprime.input.dvi ${DOC}/kafile.input.dvi \
- ${DOC}/kamke0.input.dvi \
+ ${DOC}/kamke0.input.dvi ${DOC}/kamke1.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/kamke1.input.pamphlet b/src/input/kamke1.input.pamphlet
new file mode 100644
index 0000000..2b5237a
--- /dev/null
+++ b/src/input/kamke1.input.pamphlet
@@ -0,0 +1,2124 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/src/input kamke1.input}
+\author{Timothy Daly}
+\maketitle
+\begin{abstract}
+This is the next 50 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 kamke1.output
+)set break resume
+)set mes auto off
+)clear all
+
+--S 1 of 123
+y:=operator 'y
+--R
+--R
+--R (1) y
+--R Type:
BasicOperator
+--E 1
+
+--S 2 of 123
+f := operator 'f
+--R
+--R (2) f
+--R Type:
BasicOperator
+--E 2
+
+--S 3 of 123
+g := operator 'g
+--R
+--R (3) g
+--R Type:
BasicOperator
+--E 3
+
+--S 4 of 123
+h := operator 'h
+--R
+--R (4) h
+--R Type:
BasicOperator
+--E 4
+
+--S 5 of 123
+ode51 := D(y(x),x) - (y(x)-f(x))*(y(x)-g(x))*(y(x)-(a*f(x)+b*g(x))/(a+b))*h(x)_
+ - D(f(x),x)*(y(x)-g(x))/(f(x)-g(x)) _
+ - D(g(x),x)*(y(x)-f(x))/(g(x)-f(x))
+--R
+--R (5)
+--R , ,
+--R ((b + a)g(x) + (- b - a)f(x))y (x) + ((- b - a)y(x) + (b + a)f(x))g
(x)
+--R
+--R +
+--R ,
+--R ((b + a)y(x) + (- b - a)g(x))f (x)
+--R
+--R +
+--R 3
+--R ((- b - a)g(x) + (b + a)f(x))h(x)y(x)
+--R +
+--R 2 2 2
+--R ((2b + a)g(x) + (- b + a)f(x)g(x) + (- b - 2a)f(x) )h(x)y(x)
+--R +
+--R 3 2 2 3
+--R (- b g(x) + (- b - 2a)f(x)g(x) + (2b + a)f(x) g(x) + a f(x)
)h(x)y(x)
+--R +
+--R 3 2 2 3
+--R (b f(x)g(x) + (- b + a)f(x) g(x) - a f(x) g(x))h(x)
+--R /
+--R (b + a)g(x) + (- b - a)f(x)
+--R Type: Expression
Integer
+--E 5
+
+--S 6 of 123
+ode51a:=solve(ode51,y,x)
+--R
+--R (6) "failed"
+--R Type:
Union("failed",...)
+--E 6
+
+--S 7 of 123
+ode52 := D(y(x),x) - a*y(x)**n - b*x**(n/(1-n))
+--R
+--R n
+--R - -----
+--R , n n - 1
+--R (7) y (x) - a y(x) - b x
+--R
+--R Type: Expression
Integer
+--E 7
+
+--S 8 of 123
+ode52a:=solve(ode52,y,x)
+--R
+--R (8) "failed"
+--R Type:
Union("failed",...)
+--E 8
+
+--S 9 of 123
+ode53 := D(y(x),x) - f(x)**(1-n)*D(g(x),x)*y(x)**n/(a*g(x)+b)**n _
+ - D(f(x),x)*y(x)/f(x) - f(x)*D(g(x),x)
+--R
+--R (9)
+--R n ,
+--R f(x)(a g(x) + b) y (x)
+--R
+--R +
+--R - n + 1 n 2 n , n
,
+--R (- f(x)f(x) y(x) - f(x) (a g(x) + b) )g (x) - y(x)(a g(x) + b)
f (x)
+--R
+--R /
+--R n
+--R f(x)(a g(x) + b)
+--R Type: Expression
Integer
+--E 9
+
+--S 10 of 123
+ode53a:=solve(ode53,y,x)
+--R
+--R (10) "failed"
+--R Type:
Union("failed",...)
+--E 10
+
+--S 11 of 123
+ode54 := D(y(x),x) - a**n*f(x)**(1-n)*D(g(x),x)*y(x)**n - _
+ D(f(x),x)*y(x)/f(x) - f(x)*D(g(x),x)
+--R
+--R , n - n + 1 n 2 , ,
+--R f(x)y (x) + (- f(x)a f(x) y(x) - f(x) )g (x) - y(x)f (x)
+--R
+--R (11) ---------------------------------------------------------------
+--R f(x)
+--R Type: Expression
Integer
+--E 11
+
+--S 12 of 123
+ode54a:=solve(ode54,y,x)
+--R
+--R (12) "failed"
+--R Type:
Union("failed",...)
+--E 12
+
+--S 13 of 123
+ode55 := D(y(x),x) - f(x)*y(x)**n - g(x)*y(x) - h(x)
+--R
+--R , n
+--R (13) y (x) - f(x)y(x) - g(x)y(x) - h(x)
+--R
+--R Type: Expression
Integer
+--E 13
+
+--S 14 of 123
+ode55a:=solve(ode55,y,x)
+--R
+--R (14) "failed"
+--R Type:
Union("failed",...)
+--E 14
+
+--S 15 of 123
+ode56 := D(y(x),x) - f(x)*y(x)**a - g(x)*y(x)**b
+--R
+--R , b a
+--R (15) y (x) - g(x)y(x) - f(x)y(x)
+--R
+--R Type: Expression
Integer
+--E 15
+
+--S 16 of 123
+ode5a:=solve(ode56,y,x)
+--R
+--R (16) "failed"
+--R Type:
Union("failed",...)
+--E 16
+
+--S 17 of 123
+ode57 := D(y(x),x) - sqrt(abs(y(x)))
+--R
+--R +---------+ ,
+--R (17) - \|abs(y(x)) + y (x)
+--R
+--R Type: Expression
Integer
+--E 17
+
+--S 18 of 123
+yx:=solve(ode57,y,x)
+--R
+--R +---------+
+--R - x\|abs(y(x)) + 2y(x)
+--R (18) -----------------------
+--R +----+
+--R \|y(x)
+--R Type: Union(Expression
Integer,...)
+--E 18
+
+--S 19 of 123
+ode57expr := D(yx,x) - sqrt(abs(yx))
+--R
+--R (19)
+--R +--------------------------+
+--R | +---------+
+--R +----+ +---------+ | x\|abs(y(x)) - 2y(x) ,
+---------+
+--R - \|y(x) \|abs(y(x)) |abs(---------------------) + y (x)\|abs(y(x))
+--R | +----+
+--R \| \|y(x)
+--R +
+--R - abs(y(x))
+--R /
+--R +----+ +---------+
+--R \|y(x) \|abs(y(x))
+--R Type: Expression
Integer
+--E 19
+
+--S 20 of 123
+ode58 := D(y(x),x) - a*sqrt(y(x)) - b*x
+--R
+--R , +----+
+--R (20) y (x) - a\|y(x) - b x
+--R
+--R Type: Expression
Integer
+--E 20
+
+--S 21 of 123
+ode58a:=solve(ode58,y,x)
+--R
+--R (21) "failed"
+--R Type:
Union("failed",...)
+--E 21
+
+-- this never finishes
+-- ode59 := D(y(x),x) - a*sqrt(y(x)**2+1) - b
+--
+
+--S 22 of 123
+ode60 := D(y(x),x) - sqrt(y(x)**2-1)/sqrt(x**2-1)
+--R
+--R +------+ +---------+
+--R | 2 , | 2
+--R \|x - 1 y (x) - \|y(x) - 1
+--R
+--R (22) -----------------------------
+--R +------+
+--R | 2
+--R \|x - 1
+--R Type: Expression
Integer
+--E 22
+
+--S 23 of 123
+ode60a:=solve(ode60,y,x)
+--R
+--R (23) "failed"
+--R Type:
Union("failed",...)
+--E 23
+
+--S 24 of 123
+ode61 := D(y(x),x) - sqrt(x**2-1)/sqrt(y(x)**2-1)
+--R
+--R +---------+ +------+
+--R | 2 , | 2
+--R \|y(x) - 1 y (x) - \|x - 1
+--R
+--R (24) -----------------------------
+--R +---------+
+--R | 2
+--R \|y(x) - 1
+--R Type: Expression
Integer
+--E 24
+
+--S 25 of 123
+yx:=solve(ode61,y,x)
+--R
+--R (25)
+--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 25
+
+--S 26 of 123
+ode61expr := D(yx,x) - sqrt(x**2-1)/sqrt(yx**2-1)
+--R
+--R (26)
+--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
+--R +
+--R 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
+--R +
+--R - 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 *
+--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
+------+
+--R 3 4 3 2 3 | 2
+--R ((- 64x + 32x)y(x) + (64x - 32x)y(x) - 8x + 4x)\|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 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 -
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
+------+
+--R 3 4 3 2 3 | 2
+--R ((- 64x + 32x)y(x) + (64x - 32x)y(x) - 8x + 4x)\|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 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 Type: Expression
Integer
+--E 26
+
+--S 27 of 123
+ode62 := D(y(x),x) - (y(x)-x**2*sqrt(x**2-y(x)**2))/_
+ (x*y(x)*sqrt(x**2-y(x)**2)+x)
+--R
+--R +------------+ +------------+
+--R | 2 2 , 2 | 2 2
+--R (x y(x)\|- y(x) + x + x)y (x) + x \|- y(x) + x - y(x)
+--R
+--R (27) -----------------------------------------------------------
+--R +------------+
+--R | 2 2
+--R x y(x)\|- y(x) + x + x
+--R Type: Expression
Integer
+--E 27
+
+--S 28 of 123
+ode62a:=solve(ode62,y,x)
+--R
+--R (28) "failed"
+--R Type:
Union("failed",...)
+--E 28
+
+--S 29 of 123
+ode63 := D(y(x),x) - (1+ y(x)**2)/(abs(y(x)+sqrt(1+y(x)))*sqrt(1+x)**3)
+--R
+--R +-----+ , +--------+ 2
+--R (x + 1)\|x + 1 y (x)abs(\|y(x) + 1 + y(x)) - y(x) - 1
+--R
+--R (29) -------------------------------------------------------
+--R +-----+ +--------+
+--R (x + 1)\|x + 1 abs(\|y(x) + 1 + y(x))
+--R Type: Expression
Integer
+--E 29
+
+--S 30 of 123
+ode63a:=solve(ode63,y,x)
+--R
+--R (30) "failed"
+--R Type:
Union("failed",...)
+--E 30
+
+--S 31 of 123
+ode64 := D(y(x),x) - sqrt((a*y(x)**2+b*y(x)+c)/(a*x**2+b*x+c))
+--R
+--R +--------------------+
+--R | 2
+--R , |a y(x) + b y(x) + c
+--R (31) y (x) - |--------------------
+--R | 2
+--R \| a x + b x + c
+--R Type: Expression
Integer
+--E 31
+
+--S 32 of 123
+yx:=solve(ode64,y,x)
+--R
+--R (32)
+--R log
+--R +--------------------+
+--R | 2
+--R 2 2 +-+ |a y(x) + b y(x) + c
+--R (2a x + 2a b x + 2a c)\|a |--------------------
+--R | 2
+--R \| a x + b x + c
+--R *
+--R +--------------------+
+--R | 2
+--R \|a y(x) + b y(x) + c
+--R +
+--R 3 3 2 2 2 2
+--R (- 2a x - 2a b x - 2a c x)y(x)
+--R +
+--R 2 3 2 2 2 3 2
+--R (- 2a b x - 2a b x - 2a b c x)y(x) - 2a c x - 2a b c x
+--R +
+--R 2
+--R - 2a c x
+--R *
+--R +-------------------------+
+--R | 2 2
+--R \|a c y(x) + b c y(x) + c
+--R +
+--R 3 4 2 3 2 2 2 3 2
+--R (- a x - a b x - 2a c x - a b c x - a c - a )y(x)
+--R +
+--R 2 4 2 3 2 2 2 2
+--R (- a b x - a b x - 2a b c x - b c x - b c - a b)y(x)
+--R +
+--R 2 4 3 2 2 2 3 2
+--R - a c x - a b c x - 2a c x - b c x - c - a c
+--R *
+--R +--------------------+
+--R +-+ | 2
+--R \|a \|a y(x) + b y(x) + c
+--R +
+--R 4 3 3 2 3 2
+--R (2a x + 2a b x + 2a c x)y(x)
+--R +
+--R 3 3 2 2 2 2 3 3 2 2
+--R (2a b x + 2a b x + 2a b c x)y(x) + 2a c x + 2a b c x
+--R +
+--R 2 2
+--R 2a c x
+--R *
+--R +--------------------+
+--R | 2
+--R |a y(x) + b y(x) + c
+--R |--------------------
+--R | 2
+--R \| a x + b x + c
+--R /
+--R +--------------------+
+--R | 2
+--R 2 2 |a y(x) + b y(x) + c
+--R (2a x + 2a b x + 2a c) |--------------------
+--R | 2
+--R \| a x + b x + c
+--R *
+--R +-------------------------+
+--R | 2 2
+--R \|a c y(x) + b c y(x) + c
+--R +
+--R 3 4 2 3 2 3 2
+--R (a x + a b x - a b c x - a c - a )y(x)
+--R +
+--R 2 4 2 3 2 2 2 2 4 3
+--R (a b x + a b x - b c x - b c - a b)y(x) + a c x + a b c x
+--R +
+--R 2 3 2
+--R - b c x - c - a c
+--R +
+--R log
+--R +--------------------+
+--R +-+ +-+ | 2 +-+
+--R (2\|a \|c - 2a y(x))\|a y(x) + b y(x) + c + 2a y(x)\|c
+--R +
+--R 2 +-+
+--R (- 2a y(x) - b y(x) - 2c)\|a
+--R /
+--R +--------------------+
+--R +-+ | 2
+--R 2\|c \|a y(x) + b y(x) + c - b y(x) - 2c
+--R /
+--R +-+
+--R \|a
+--R Type: Union(Expression
Integer,...)
+--E 32
+
+@
+The results of this substitution are too long to include.
+It should be zero but Axiom cannot simplify it.
+<<*>>=
+--S 33 of 123
+ode64expr := D(yx,x) - sqrt((a*yx**2+b*yx+c)/(a*x**2+b*x+c));
+--E 33
+
+--S 34 of 123
+ode65 := D(y(x),x) - sqrt((y(x)**3+1)/(x**3+1))
+--R
+--R +---------+
+--R | 3
+--R , |y(x) + 1
+--R (34) y (x) - |---------
+--R | 3
+--R \| x + 1
+--R Type: Expression
Integer
+--E 34
+
+--S 35 of 123
+ode65a:=solve(ode65,y,x)
+--R
+--R +---------+
+--R | 3
+--R |y(x) + 1
+--R |---------
+--R x | 3 y(x)
+--I ++ \| %P + 1 ++ 1
+--I (35) | - ------------ d%P + | ---------- d%P
+--R ++ +---------+ ++ +-------+
+--R | 3 | 3
+--I \|y(x) + 1 \|%P + 1
+--R Type: Union(Expression
Integer,...)
+--E 35
+
+--S 36 of 123
+ode66 := D(y(x),x) - sqrt(abs(y(x)*(1-y(x))*(1-a*y(x))))/_
+ sqrt(abs(x*(1-x)*(1-a*x)))
+--R
+--R (36)
+--R +------------------------------------+
+--R | 3 2
+--R - \|abs(a y(x) + (- a - 1)y(x) + y(x))
+--R +
+--R +---------------------------+
+--R | 3 2 ,
+--R \|abs(a x + (- a - 1)x + x) y (x)
+--R
+--R /
+--R +---------------------------+
+--R | 3 2
+--R \|abs(a x + (- a - 1)x + x)
+--R Type: Expression
Integer
+--E 36
+
+--S 37 of 123
+ode66a:=solve(ode66,y,x)
+--R
+--R (37) "failed"
+--R Type:
Union("failed",...)
+--E 37
+
+--S 38 of 123
+ode67 := D(y(x),x) - sqrt(1-y(x)**4)/sqrt(1-x**4)
+--R
+--R +--------+ +-----------+
+--R | 4 , | 4
+--R \|- x + 1 y (x) - \|- y(x) + 1
+--R
+--R (38) ---------------------------------
+--R +--------+
+--R | 4
+--R \|- x + 1
+--R Type: Expression
Integer
+--E 38
+
+--S 39 of 123
+ode67a:=solve(ode67,y,x)
+--R
+--R (39) "failed"
+--R Type:
Union("failed",...)
+--E 39
+
+--S 40 of 123
+ode68 := D(y(x),x) - sqrt((a*y(x)**4+b*y(x)**2+1)/(a*x**4+b*x**2+1))
+--R
+--R +---------------------+
+--R | 4 2
+--R , |a y(x) + b y(x) + 1
+--R (40) y (x) - |---------------------
+--R | 4 2
+--R \| a x + b x + 1
+--R Type: Expression
Integer
+--E 40
+
+--S 41 of 123
+ode68a:=solve(ode68,y,x)
+--R
+--R
+--R (41)
+--R +---------------------+
+--R | 4 2
+--R |a y(x) + b y(x) + 1
+--R |---------------------
+--R x | 2 4 y(x)
+--I ++ \| %N b + %N a + 1 ++ 1
+--I | - ------------------------ d%N + | ------------------ d%N
+--R ++ +---------------------+ ++ +---------------+
+--R | 4 2 | 2 4
+--I \|a y(x) + b y(x) + 1 \|%N b + %N a + 1
+--R Type: Union(Expression
Integer,...)
+--E 41
+
+--S 42 of 123
+ode69 := D(y(x),x) - sqrt((b4*y(x)**4+b3*y(x)**3+b2*y(x)**2+b1*y(x)+b0)*_
+ (a4*x**4+a3*x**3+a2*x**2+a1*x+a0))
+--R
+--R
+--R (42)
+--R ,
+--R y (x)
+--R
+--R +
+--R -
+--R ROOT
+--R 4 3 2 4
+--R (a4 b4 x + a3 b4 x + a2 b4 x + a1 b4 x + a0 b4)y(x)
+--R +
+--R 4 3 2 3
+--R (a4 b3 x + a3 b3 x + a2 b3 x + a1 b3 x + a0 b3)y(x)
+--R +
+--R 4 3 2 2
+--R (a4 b2 x + a3 b2 x + a2 b2 x + a1 b2 x + a0 b2)y(x)
+--R +
+--R 4 3 2
4
+--R (a4 b1 x + a3 b1 x + a2 b1 x + a1 b1 x + a0 b1)y(x) + a4 b0
x
+--R +
+--R 3 2
+--R a3 b0 x + a2 b0 x + a1 b0 x + a0 b0
+--R Type: Expression
Integer
+--E 42
+
+--S 43 of 123
+ode69a:=solve(ode69,y,x)
+--R
+--R
+--R >> Error detected within library code:
+--R PFO::possibleOrder: more than 1 algebraic constant
+--R
+--R Continuing to read the file...
+--R
+--E 43
+
+--S 44 of 123
+ode70 := D(y(x),x) - sqrt((a4*x**4+a3*x**3+a2*x**2+a1*x+a0)/_
+ (b4*y(x)**4+b3*y(x)**3+b2*y(x)**2+b1*y(x)+b0))
+--R
+--R +---------------------------------------------+
+--R | 4 3 2
+--R , | a4 x + a3 x + a2 x + a1 x + a0
+--R (43) y (x) - |---------------------------------------------
+--R | 4 3 2
+--R \|b4 y(x) + b3 y(x) + b2 y(x) + b1 y(x) + b0
+--R Type: Expression
Integer
+--E 44
+
+--S 45 of 123
+ode70a:=solve(ode70,y,x)
+--R
+--R
+--R >> Error detected within library code:
+--R PFO::possibleOrder: more than 1 algebraic constant
+--R
+--R Continuing to read the file...
+--R
+--E 45
+
+--S 46 of 123
+ode71 := D(y(x),x) - sqrt((b4*y(x)**4+b3*y(x)**3+b2*y(x)**2+b1*y(x)+b0)/_
+ (a4*x**4+a3*x**3+a2*x**2+a1*x+a0))
+--R
+--R +---------------------------------------------+
+--R | 4 3 2
+--R , |b4 y(x) + b3 y(x) + b2 y(x) + b1 y(x) + b0
+--R (44) y (x) - |---------------------------------------------
+--R | 4 3 2
+--R \| a4 x + a3 x + a2 x + a1 x + a0
+--R Type: Expression
Integer
+--E 46
+
+--S 47 of 123
+ode71a:=solve(ode71,y,x)
+--R
+--R
+--R (45)
+--R +---------------------------------------------+
+--R | 4 3 2
+--R |b4 y(x) + b3 y(x) + b2 y(x) + b1 y(x) + b0
+--R |---------------------------------------------
+--R x | 4 3 2
+--I ++ \| %N a4 + %N a3 + %N a2 + %N a1 + a0
+--I | - ------------------------------------------------ d%N
+--R ++ +---------------------------------------------+
+--R | 4 3 2
+--R \|b4 y(x) + b3 y(x) + b2 y(x) + b1 y(x) + b0
+--R +
+--R y(x)
+--R ++ 1
+--I | ------------------------------------- d%N
+--R ++ +----------------------------------+
+--R | 4 3 2
+--I \|%N b4 + %N b3 + %N b2 + %N b1 + b0
+--R Type: Union(Expression
Integer,...)
+--E 47
+
+--S 48 of 123
+R1:=operator 'R1
+--R
+--R (46) R1
+--R Type:
BasicOperator
+--E 48
+
+--S 49 of 123
+R2:=operator 'R2
+--R
+--R (47) R2
+--R Type:
BasicOperator
+--E 49
+
+--S 50 of 123
+ode72 := D(y(x),x) - R1(x,sqrt(a4*x**4+a3*x**3+a2*x**2+a1*x+a0))*_
+ R2(y(x),sqrt(b4*y(x)**4+b3*y(x)**3+b2*y(x)**2+b1*y(x)+b0))
+--R
+--R (48)
+--R -
+--R +---------------------------------+
+--R | 4 3 2
+--R R1(x,\|a4 x + a3 x + a2 x + a1 x + a0 )
+--R *
+--R +---------------------------------------------+
+--R | 4 3 2
+--R R2(y(x),\|b4 y(x) + b3 y(x) + b2 y(x) + b1 y(x) + b0 )
+--R +
+--R ,
+--R y (x)
+--R
+--R Type: Expression
Integer
+--E 50
+
+--S 51 of 123
+ode72a:=solve(ode72,y,x)
+--R
+--R >> Error detected within library code:
+--R Function not supported by Risch d.e.
+--R
+--R Continuing to read the file...
+--R
+--E 51
+
+--S 52 of 123
+ode73 := D(y(x),x) - ((a3*x**3+a2*x**2+a1*x+a0)/_
+ (a3*y(x)**3+a2*y(x)**2+a1*y(x)+a0))**(2/3)
+--R
+--R +----------------------------------+2
+--R | 3 2
+--R , | a3 x + a2 x + a1 x + a0
+--R (49) y (x) - |----------------------------------
+--R 3| 3 2
+--R \|a3 y(x) + a2 y(x) + a1 y(x) + a0
+--R Type: Expression
Integer
+--E 52
+
+@
+Attempting to solve this problem fails with the error:
+\begin{verbatim}
+ode73a:=solve(ode73,y,x)
+ >> Error detected within library code:
+ Table construction failed in MLIFT
+\end{verbatim}
+<<*>>=
+
+--S 53 of 123
+ode74 := D(y(x),x) - f(x)*(y(x)-g(x))*sqrt((y(x)-a)*(y(x)-b))
+--R
+--R +---------------------------+
+--R , | 2
+--R (50) y (x) + (- f(x)y(x) + f(x)g(x))\|y(x) + (- b - a)y(x) + a b
+--R
+--R Type: Expression
Integer
+--E 53
+
+--S 54 of 123
+ode74a:=solve(ode74,y,x)
+--R
+--R (51) "failed"
+--R Type:
Union("failed",...)
+--E 54
+
+--S 55 of 123
+ode75 := D(y(x),x) - exp(x-y(x)) + exp(x)
+--R
+--R , - y(x) + x x
+--R (52) y (x) - %e + %e
+--R
+--R Type: Expression
Integer
+--E 55
+
+--S 56 of 123
+ode75a:=solve(ode75,y,x)
+--R
+--R (53) "failed"
+--R Type:
Union("failed",...)
+--E 56
+
+--S 57 of 123
+ode76 := D(y(x),x) - a*cos(y(x)) + b
+--R
+--R ,
+--R (54) y (x) - a cos(y(x)) + b
+--R
+--R Type: Expression
Integer
+--E 57
+
+--S 58 of 123
+yx:=solve(ode76,y,x)
+--R
+--R (55)
+--R +---------+ +---------+
+--R 2 2 | 2 2 | 2 2
+--R (- b + a )sin(y(x)) + b\|- b + a cos(y(x)) - a\|- b + a
+--R log(-------------------------------------------------------------)
+--R a cos(y(x)) - b
+--R +
+--R +---------+
+--R | 2 2
+--R x\|- b + a
+--R /
+--R +---------+
+--R | 2 2
+--R \|- b + a
+--R Type: Union(Expression
Integer,...)
+--E 58
+
+--S 59 of 123
+ode76expr := D(yx,x) - a*cos(yx) + b
+--R
+--R (56)
+--R 2 2 4 3 3
+--R ((- a b + a )cos(y(x)) + a b - a b)sin(y(x))
+--R +
+--R +---------+ +---------+
+--R 2 | 2 2 2 2 3 | 2 2
+--R a b\|- b + a cos(y(x)) + (- a b - a )\|- b + a cos(y(x))
+--R +
+--R +---------+
+--R 2 | 2 2
+--R a b\|- b + a
+--R *
+--R cos
+--R log
+--R +---------+
+---------+
+--R 2 2 | 2 2 | 2
2
+--R (- b + a )sin(y(x)) + b\|- b + a cos(y(x)) - a\|- b
+ a
+--R
-------------------------------------------------------------
+--R a cos(y(x)) - b
+--R +
+--R +---------+
+--R | 2 2
+--R x\|- b + a
+--R /
+--R +---------+
+--R | 2 2
+--R \|- b + a
+--R +
+--R +---------+
+--R | 2 2 2 2 2
+--R - a\|- b + a sin(y(x)) + (- b + a )sin(y(x))
+--R +
+--R +---------+ +---------+
+--R | 2 2 2 | 2 2
+--R - a\|- b + a cos(y(x)) + b\|- b + a cos(y(x))
+--R *
+--R ,
+--R y (x)
+--R
+--R +
+--R 3 2 3 3 4 3 2 2 2
+--R ((a b + a b - a b - a )cos(y(x)) - b - b + a b + a b)sin(y(x))
+--R +
+--R +---------+
+--R 2 | 2 2 2
+--R (- a b - a b)\|- b + a cos(y(x))
+--R +
+--R +---------+
+---------+
+--R 3 2 2 2 | 2 2 2 | 2 2
+--R (b + b + a b + a )\|- b + a cos(y(x)) + (- a b - a b)\|- b + a
+--R /
+--R +---------+
+--R 2 3 3 2 | 2 2
2
+--R ((a b - a )cos(y(x)) - b + a b)sin(y(x)) - a b\|- b + a cos(y(x))
+--R +
+--R +---------+ +---------+
+--R 2 2 | 2 2 | 2 2
+--R (b + a )\|- b + a cos(y(x)) - a b\|- b + a
+--R Type: Expression
Integer
+--E 59
+
+--S 60 of 123
+ode77 := D(y(x),x) - cos(a*y(x)+b*x)
+--R
+--R ,
+--R (57) y (x) - cos(a y(x) + b x)
+--R
+--R Type: Expression
Integer
+--E 60
+
+--S 61 of 123
+ode77a:=solve(ode77,y,x)
+--R
+--R (58) "failed"
+--R Type:
Union("failed",...)
+--E 61
+
+--S 62 of 123
+ode78 := D(y(x),x) + a*sin(alpha*y(x)+beta*x) + b
+--R
+--R ,
+--R (59) y (x) + a sin(alpha y(x) + beta x) + b
+--R
+--R Type: Expression
Integer
+--E 62
+
+--S 63 of 123
+ode78a:=solve(ode78,y,x)
+--R
+--R (60) "failed"
+--R Type:
Union("failed",...)
+--E 63
+
+--S 64 of 123
+ode79 := D(y(x),x) + f(x)*cos(a*y(x)) + g(x)*sin(a*y(x)) + h(x)
+--R
+--R ,
+--R (61) y (x) + g(x)sin(a y(x)) + f(x)cos(a y(x)) + h(x)
+--R
+--R Type: Expression
Integer
+--E 64
+
+--S 65 of 123
+ode79a:=solve(ode79,y,x)
+--R
+--R (62) "failed"
+--R Type:
Union("failed",...)
+--E 65
+
+--S 66 of 123
+ode80 := D(y(x),x) + f(x)*sin(y(x)) + (1-D(f(x),x))*cos(y(x)) - D(f(x),x) - 1
+--R
+--R , ,
+--R (63) y (x) + (- cos(y(x)) - 1)f (x) + f(x)sin(y(x)) + cos(y(x)) - 1
+--R
+--R Type: Expression
Integer
+--E 66
+
+--S 67 of 123
+ode80a:=solve(ode80,y,x)
+--R
+--R (64) "failed"
+--R Type:
Union("failed",...)
+--E 67
+
+--S 68 of 123
+ode81 := D(y(x),x) + 2*tan(y(x))*tan(x) - 1
+--R
+--R ,
+--R (65) y (x) + 2tan(x)tan(y(x)) - 1
+--R
+--R Type: Expression
Integer
+--E 68
+
+--S 69 of 123
+ode81a:=solve(ode81,y,x)
+--R
+--R (66) "failed"
+--R Type:
Union("failed",...)
+--E 69
+
+--S 70 of 123
+ode82 := D(y(x),x) - a*(1+tan(y(x))**2) + tan(y(x))*tan(x)
+--R
+--R , 2
+--R (67) y (x) - a tan(y(x)) + tan(x)tan(y(x)) - a
+--R
+--R Type: Expression
Integer
+--E 70
+
+--S 71 of 123
+ode82a:=solve(ode82,y,x)
+--R
+--R (68) "failed"
+--R Type:
Union("failed",...)
+--E 71
+
+--S 72 of 123
+ode83 := D(y(x),x) - tan(x*y(x))
+--R
+--R ,
+--R (69) y (x) - tan(x y(x))
+--R
+--R Type: Expression
Integer
+--E 72
+
+--S 73 of 123
+ode83a:=solve(ode83,y,x)
+--R
+--R (70) "failed"
+--R Type:
Union("failed",...)
+--E 73
+
+--S 74 of 123
+ode84 := D(y(x),x) - f(a*x + b*y(x))
+--R
+--R ,
+--R (71) y (x) - f(b y(x) + a x)
+--R
+--R Type: Expression
Integer
+--E 74
+
+--S 75 of 123
+ode84a:=solve(ode84,y,x)
+--R
+--R (72) "failed"
+--R Type:
Union("failed",...)
+--E 75
+
+--S 76 of 123
+ode85 := D(y(x),x) - x**(a-1)*y(x)**(1-b)*f(x**a/a + y(x)**b/b)
+--R
+--R b a
+--R a - 1 - b + 1 a y(x) + b x ,
+--R (73) - x y(x) f(--------------) + y (x)
+--R a b
+--R Type: Expression
Integer
+--E 76
+
+--S 77 of 123
+ode85a:=solve(ode85,y,x)
+--R
+--R (74) "failed"
+--R Type:
Union("failed",...)
+--E 77
+
+--S 78 of 123
+ode86 := D(y(x),x) - (y(x)-x*f(x**2+a*y(x)**2))/(x+a*y(x)*f(x**2+a*y(x)**2))
+--R
+--R 2 2 , 2 2
+--R (a y(x)f(a y(x) + x ) + x)y (x) + x f(a y(x) + x ) - y(x)
+--R
+--R (75) -----------------------------------------------------------
+--R 2 2
+--R a y(x)f(a y(x) + x ) + x
+--R Type: Expression
Integer
+--E 78
+
+--S 79 of 123
+ode86a:=solve(ode86,y,x)
+--R
+--R (76) "failed"
+--R Type:
Union("failed",...)
+--E 79
+
+--S 80 of 123
+ode87 := D(y(x),x) - (y(x)*a*f(x**c*y(x))+c*x**a*y(x)**b)/_
+ (x*b*f(x**c*y(x))-x**a*y(x)**b)
+--R
+--R a b c , a b c
+--R (x y(x) - b x f(y(x)x ))y (x) + c x y(x) + a y(x)f(y(x)x )
+--R
+--R (77) ------------------------------------------------------------
+--R a b c
+--R x y(x) - b x f(y(x)x )
+--R Type: Expression
Integer
+--E 80
+
+--S 81 of 123
+ode87a:=solve(ode87,y,x)
+--R
+--R (78) "failed"
+--R Type:
Union("failed",...)
+--E 81
+
+--S 82 of 123
+ode88 := 2*D(y(x),x) - 3*y(x)**2 - 4*a*y(x) - b - c*exp(-2*a*x)
+--R
+--R , - 2a x 2
+--R (79) 2y (x) - c %e - 3y(x) - 4a y(x) - b
+--R
+--R Type: Expression
Integer
+--E 82
+
+--S 83 of 123
+ode88a:=solve(ode88,y,x)
+--R
+--R (80) "failed"
+--R Type:
Union("failed",...)
+--E 83
+
+--S 84 of 123
+ode89 := x*D(y(x),x) - sqrt(a**2 - x**2)
+--R
+--R +---------+
+--R , | 2 2
+--R (81) xy (x) - \|- x + a
+--R
+--R Type: Expression
Integer
+--E 84
+
+--S 85 of 123
+ode89a:=solve(ode89,y,x)
+--R
+--R (82)
+--R +---------+
+--R +---------+ | 2 2
+--R | 2 2 2 \|- x + a - a 2
+--R (a\|- x + a - a )log(----------------) - x
+--R x
+--R [particular= ----------------------------------------------,basis= [1]]
+--R +---------+
+--R | 2 2
+--R \|- x + a - a
+--RType: Union(Record(particular: Expression Integer,basis: List Expression
Integer),...)
+--E 85
+
+--S 86 of 123
+yx:=ode89a.particular
+--R
+--R +---------+
+--R +---------+ | 2 2
+--R | 2 2 2 \|- x + a - a 2
+--R (a\|- x + a - a )log(----------------) - x
+--R x
+--R (83) ----------------------------------------------
+--R +---------+
+--R | 2 2
+--R \|- x + a - a
+--R Type: Expression
Integer
+--E 86
+
+--S 87 of 123
+ode89expr := x*D(yx,x) - sqrt(a**2 - x**2)
+--R
+--R (84) 0
+--R Type: Expression
Integer
+--E 87
+
+--S 88 of 123
+ode90 := x*D(y(x),x) + y(x) - x*sin(x)
+--R
+--R ,
+--R (85) xy (x) - x sin(x) + y(x)
+--R
+--R Type: Expression
Integer
+--E 88
+
+--S 89 of 123
+ode90a:=solve(ode90,y,x)
+--R
+--R sin(x) - x cos(x) 1
+--R (86) [particular= -----------------,basis= [-]]
+--R x x
+--RType: Union(Record(particular: Expression Integer,basis: List Expression
Integer),...)
+--E 89
+
+--S 90 of 123
+yx:=ode90a.particular
+--R
+--R sin(x) - x cos(x)
+--R (87) -----------------
+--R x
+--R Type: Expression
Integer
+--E 90
+
+--S 91 of 123
+ode90expr := x*D(yx,x) + yx - x*sin(x)
+--R
+--R (88) 0
+--R Type: Expression
Integer
+--E 91
+
+--S 92 of 123
+ode91 := x*D(y(x),x) - y(x) - x/log(x)
+--R
+--R ,
+--R x log(x)y (x) - y(x)log(x) - x
+--R
+--R (89) ------------------------------
+--R log(x)
+--R Type: Expression
Integer
+--E 92
+
+--S 93 of 123
+ode91a:=solve(ode91,y,x)
+--R
+--R (90) [particular= x log(log(x)),basis= [x]]
+--RType: Union(Record(particular: Expression Integer,basis: List Expression
Integer),...)
+--E 93
+
+--S 94 of 123
+yx:=ode91a.particular
+--R
+--R (91) x log(log(x))
+--R Type: Expression
Integer
+--E 94
+
+--S 95 of 123
+ode91expr := x*D(yx,x) - yx - x/log(x)
+--R
+--R (92) 0
+--R Type: Expression
Integer
+--E 95
+
+--S 96 of 123
+ode92 := x*D(y(x),x) - y(x) - x**2*sin(x)
+--R
+--R , 2
+--R (93) xy (x) - x sin(x) - y(x)
+--R
+--R Type: Expression
Integer
+--E 96
+
+--S 97 of 123
+ode92a:=solve(ode92,y,x)
+--R
+--R (94) [particular= - x cos(x),basis= [x]]
+--RType: Union(Record(particular: Expression Integer,basis: List Expression
Integer),...)
+--E 97
+
+--S 98 of 123
+yx:=ode92a.particular
+--R
+--R (95) - x cos(x)
+--R Type: Expression
Integer
+--E 98
+
+--S 99 of 123
+ode92expr := x*D(yx,x) - yx - x**2*sin(x)
+--R
+--R (96) 0
+--R Type: Expression
Integer
+--E 99
+
+
+--S 100 of 123
+ode93 := x*D(y(x),x) - y(x) - x*cos(log(log(x)))/log(x)
+--R
+--R ,
+--R - x cos(log(log(x))) + x log(x)y (x) - y(x)log(x)
+--R
+--R (97) -------------------------------------------------
+--R log(x)
+--R Type: Expression
Integer
+--E 100
+
+--S 101 of 123
+ode93a:=solve(ode93,y,x)
+--R
+--R (98) [particular= x sin(log(log(x))),basis= [x]]
+--RType: Union(Record(particular: Expression Integer,basis: List Expression
Integer),...)
+--E 101
+
+--S 102 of 123
+yx:=ode93a.particular
+--R
+--R (99) x sin(log(log(x)))
+--R Type: Expression
Integer
+--E 102
+
+--S 103 of 123
+ode93 := x*D(yx,x) - yx - x*cos(log(log(x)))/log(x)
+--R
+--R (100) 0
+--R Type: Expression
Integer
+--E 103
+
+--S 104 of 123
+ode94 := x*D(y(x),x) +a*y(x) + b*x**n
+--R
+--R , n
+--R (101) xy (x) + b x + a y(x)
+--R
+--R Type: Expression
Integer
+--E 104
+
+--S 105 of 123
+ode94a:=solve(ode94,y,x)
+--R
+--R n log(x)
+--R b %e - a log(x)
+--R (102) [particular= - ------------,basis= [%e ]]
+--R n + a
+--RType: Union(Record(particular: Expression Integer,basis: List Expression
Integer),...)
+--E 105
+
+--S 106 of 123
+yx:=ode94a.particular
+--R
+--R n log(x)
+--R b %e
+--R (103) - ------------
+--R n + a
+--R Type: Expression
Integer
+--E 106
+
+--S 107 of 123
+ode94expr := x*D(yx,x) +a*yx + b*x**n
+--R
+--R n log(x) n
+--R (104) - b %e + b x
+--R Type: Expression
Integer
+--E 107
+
+--S 108 of 123
+exprule := rule x^n == %e^(n*log(x))
+--R
+--R n n log(x)
+--R (105) x == %e
+--R Type: RewriteRule(Integer,Integer,Expression
Integer)
+--E 108
+
+--S 109 of 123
+exprule ode94expr
+--R
+--R (106) 0
+--R Type: Expression
Integer
+--E 109
+
+--S 110 of 123
+ode95 := x*D(y(x),x) + y(x)**2 + x**2
+--R
+--R , 2 2
+--R (107) xy (x) + y(x) + x
+--R
+--R Type: Expression
Integer
+--E 110
+
+--S 111 of 123
+ode95a:=solve(ode95,y,x)
+--R
+--R
+--R (108) "failed"
+--R Type:
Union("failed",...)
+--E 111
+
+--S 112 of 123
+ode96 := x*D(y(x),x) - y(x)**2 + 1
+--R
+--R
+--R , 2
+--R (109) xy (x) - y(x) + 1
+--R
+--R Type: Expression
Integer
+--E 112
+
+--S 113 of 123
+yx:=solve(ode96,y,x)
+--R
+--R - x y(x) - x
+--R (110) ----------------------
+--R +--------+ +--------+
+--R \|y(x) - 1 \|y(x) + 1
+--R Type: Union(Expression
Integer,...)
+--E 113
+
+--S 114 of 123
+ode96expr := x*D(yx,x) - yx**2 + 1
+--R
+--R (111)
+--R 2 , 2 2 +--------+ +--------+ 2
+--R x y (x) + ((- x + 1)y(x) - x - 1)\|y(x) - 1 \|y(x) + 1 - x y(x) + x
+--R
+--R -----------------------------------------------------------------------
+--R +--------+ +--------+
+--R (y(x) - 1)\|y(x) - 1 \|y(x) + 1
+--R Type: Expression
Integer
+--E 114
+
+--S 115 of 123
+ode97 := x*D(y(x),x) + a*y(x)**2 - y(x) + b*x**2
+--R
+--R
+--R , 2 2
+--R (112) xy (x) + a y(x) - y(x) + b x
+--R
+--R Type: Expression
Integer
+--E 115
+
+--S 116 of 123
+yx:=solve(ode97,y,x)
+--R
+--R
+--R +------+
+--R a y(x)\|- 4a b - 2a b x
+--R (113) ---------------------------------------
+--R +-----+
+--R +------+ 2x\|- a b
+--R (2b x\|- 4a b - 4a b y(x))%e
+--R Type: Union(Expression
Integer,...)
+--E 116
+
+--S 117 of 123
+ode97expr := x*D(yx,x) + a*yx**2 - yx + b*x**2
+--R
+--R (114)
+--R +-----+
+--R 3 +------+ 2 2 2x\|- a b ,
+--R (- 4a b x \|- 4a b + 8a b x y(x))%e y (x)
+--R
+--R +
+--R 2 3 2 3 5 +------+ 2 2 2 3 3 4
+--R ((12a b x y(x) - 4b x )\|- 4a b - 8a b x y(x) + 24a b x y(x))
+--R *
+--R +-----+ 2
+--R 2x\|- a b
+--R (%e )
+--R +
+--R 2 3 3 +------+ 2 2 2 2 4
+--R ((- 4a x y(x) - 4a b x y(x))\|- 4a b - 8a b x y(x) - 8a b x
)
+--R *
+--R +-----+
+--R \|- a b
+--R +
+--R 2 3 2 +------+ 2 2 2 3
+--R (- 2a y(x) + 2a b x y(x))\|- 4a b - 12a b x y(x) - 4a b x
+--R *
+--R +-----+
+--R 2x\|- a b
+--R %e
+--R +
+--R 3 2 2 3 +------+ 4 3 3 2
+--R (a x y(x) + a b x )\|- 4a b + 2a y(x) + 2a b x y(x)
+--R /
+--R 2 2 3 +------+ 2 3 2 2
+--R ((12a b x y(x) - 4b x )\|- 4a b - 8a b y(x) + 24a b x y(x))
+--R *
+--R +-----+ 2
+--R 2x\|- a b
+--R (%e )
+--R Type: Expression
Integer
+--E 117
+
+--S 118 of 123
+ode98 := x*D(y(x),x) + a*y(x)**2 - b*y(x) + c*x**(2*b)
+--R
+--R
+--R , 2b 2
+--R (115) xy (x) + c x + a y(x) - b y(x)
+--R
+--R Type: Expression
Integer
+--E 118
+
+--S 119 of 123
+ode98a:=solve(ode98,y,x)
+--R
+--R (116) "failed"
+--R Type:
Union("failed",...)
+--E 119
+
+--S 120 of 123
+ode99 := x*D(y(x),x) + a*y(x)**2 - b*y(x) - c*x**beta
+--R
+--R
+--R , beta 2
+--R (117) xy (x) - c x + a y(x) - b y(x)
+--R
+--R Type: Expression
Integer
+--E 120
+
+--S 121 of 123
+ode99a:=solve(ode99,y,x)
+--R
+--R
+--R (118) "failed"
+--R Type:
Union("failed",...)
+--E 121
+
+--S 122 of 123
+ode100 := x*D(y(x),x) + x*y(x)**2 + a
+--R
+--R
+--R , 2
+--R (119) xy (x) + x y(x) + a
+--R
+--R Type: Expression
Integer
+--E 122
+
+--S 123 of 123
+ode100a:=solve(ode100,y,x)
+--R
+--R
+--R (120) "failed"
+--R Type:
Union("failed",...)
+--E 123
+)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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