# linear differential equation - periodic solutions

• Aug 23rd 2012, 07:32 AM
NFS1
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?
• Aug 23rd 2012, 07:37 AM
HallsofIvy
Re: linear differential equation - periodic solutions
If and only if the matrix A has pure imaginary eigenvalues.
• Aug 26th 2012, 04:46 AM
NFS1
Re: linear differential equation - periodic solutions
Quote:

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
• Aug 26th 2012, 04:55 AM
Prove It
Re: linear differential equation - periodic solutions
Quote:

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...
• Aug 27th 2012, 04:15 PM
NFS1
Re: linear differential equation - periodic solutions
Quote:

Originally Posted by Prove It
You are probably expected to prove this result...

How would i prove that they have pure imaginary eigenvalues? :S