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Math Help - linear differential equation - periodic solutions

  1. #1
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    linear differential equation - periodic solutions

    Under what conditions on the matrix A can the linear differential equation dx/dt = Ax where x = (x1,x2....,xn)^T have periodic solutions?
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  2. #2
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    Re: linear differential equation - periodic solutions

    If and only if the matrix A has pure imaginary eigenvalues.
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  3. #3
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    Re: linear differential equation - periodic solutions

    Quote Originally Posted by HallsofIvy View Post
    If and only if the matrix A has pure imaginary eigenvalues.
    Is that the only condition? A 4 mark question thought it would have abit more to it
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  4. #4
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    Re: linear differential equation - periodic solutions

    Quote Originally Posted by NFS1 View Post
    Is that the only condition? A 4 mark question thought it would have abit more to it
    You are probably expected to prove this result...
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  5. #5
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    Re: linear differential equation - periodic solutions

    Quote Originally Posted by Prove It View Post
    You are probably expected to prove this result...
    How would i prove that they have pure imaginary eigenvalues? :S
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