# Thread: linear differential equation - periodic solutions

1. ## 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?

2. ## Re: linear differential equation - periodic solutions

If and only if the matrix A has pure imaginary eigenvalues.

3. ## Re: linear differential equation - periodic solutions

Originally Posted by HallsofIvy
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

4. ## Re: linear differential equation - periodic solutions

Originally Posted by NFS1
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...

5. ## Re: linear differential equation - periodic solutions

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