1. The problem statement, all variables and given/known data Consider the system x' + x = F(t), where F is smooth, T-periodic function. IS it true that the system necessarily has a stable T-periodic solution x(t)? If so, Prove it; If not, find an F that provides a counterexample. 2. Relevant equations x' + x = F(t) 3. The attempt at a solution So, I think this system necessarily have a T-periodic solution x(t). To prove it, I let y = t so i can eliminate the time parameter from the equation so then I get a 2D system x' = F(y) - x y' = 1 SO, then I plan to find a poincare map so that showing that x(t) is T-periodic. MY question is, before I go further, is this a good approach to the problem? thanks.