Direct Integration of Matrices

[jcw]

I am working on mechanical systems dynamics.  I have a system state equation in
the time domain:

        x' = Ax + Bu

Where:
        A is (n x n) and is known
        x is (n x 1) is unknown
        B is (n x r) is known
        u is (r x 1) is known u = u(t) and is the input to the system

I realize that I could do this one row at a time by hand (so to speak), but I am
trying to generalize to large-ish values of n.

My dynamics text tells me that I can solve the system state, x, by direct
integration of x'.

        x = x_0 + INT ( Ax + Bu ) dt

Does octave provide a method of solving this matrix of diff eq's directly?
Nothing stood out as the function I needed while reading the docs.  The one 
thing
that seemed pertinent is 

        "Octave does not have built-in functions for computing the integral of 
functions
of multiple variables directly."

Am I stuck writing my own loops for this problem?  I've done some numerical
integration in the past.  I'd like to use a built-in method if one is available.
Don't assume I know what I'm doing.  It's been a while since college. I may well
have overlooked something obvious to a person who has lots of practice.

Thanks,
Jason C. Wells