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How to solve linear first order variable coefficient systems?

  1. Sep 21, 2012 #1
    1. how do i solve
    X'(t)=A(t)X(t)




    2. Relevant 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.

    3. 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: Sep 21, 2012
  2. jcsd
  3. Sep 21, 2012 #2
    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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