# Homework Help: System of DEs

1. Dec 14, 2011

### namu

I am confused on how to solve the following problem.

Consider the system

$\vec{x}$t=A$\vec{x}$+$\vec{f}$

where $\vec{x}$, $\vec{f}$ are vectors of size n and A is a
constant nxn matrix. Characterize all matrices A so that for all periodic functions
$\vec{f}$ (irrespective of period) there will be at most one periodic solution.

I think we want no complex eigenvalues for the homogenous solution to have no
periodic solutions, however am not sure and am lost with the forcing function.