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Math Help - Question regarding a system of DE's and eigenvalues.

  1. #1
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    Question regarding a system of DE's and eigenvalues.

    Dear Colleagues,

    Could you please help me in solving the following problem:
    Show that if w is not an eigenvalue of an n\times n constant matrix A, then x(t) = k e^{wt} is a solution of
    x^{\prime}(t) = A x(t) - b e^{wt},
    where b and k are n\times 1 constant vectors.


    Best Regards,

    Raed.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Substitute x =k e^{ wt } in the equation. You'll obtain wk = Ak - b .

    If w is not an eigenvalue of A then, you can choose k = (A-w I )^{ -1 } b .
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