How to solve linear first order variable coefficient systems?

  • Thread starter robijnix
  • Start date
  • #1
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1. how do i solve
X'(t)=A(t)X(t)




Homework Equations


I know of this equation:
[itex]x(t) = x_0 \exp\left( \int_{t_0}^t f(\xi) \, d\xi \right)[/itex]

but i think that i'm using it wrong.

The Attempt at a Solution


i have the following mathematica code:
A=
fIVwe.png

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:

Answers and Replies

  • #2
4
0
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
 

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