How to solve linear first order variable coefficient systems?

1. Sep 21, 2012

robijnix

1. how do i solve
X'(t)=A(t)X(t)

2. Relevant equations
I know of this equation:
$x(t) = x_0 \exp\left( \int_{t_0}^t f(\xi) \, d\xi \right)$

but i think that i'm using it wrong.

3. The attempt at a solution
i have the following mathematica code:
A=
x = MatrixExp[Integrate[A, {t, 0, s}]].{1, 0,0,0};
Plot[x[[2]] + x[[4]], {s, 0, 500}]

the problem is, that the result i get it not the same as when i numerically plot it with matlab, wich leads me to believe that i'm doing something wrong.

any kind of help would be greatly appreciated,

Thanks

Last edited: Sep 21, 2012
2. Sep 21, 2012

robijnix

Never mind i found out the problem.

my matrix A doesnt statisfy A(t1)A(t2)=A(t2)A(t1), in wich case the above formula is not valid