Consider a differential equation x=Ax+b(t) with xRn and b:RRn continuous and of period >0, that is, b(t+)=b(t) for some >0. (a) Assume the following condition on the matrix A holds: If is an eigenvalue of A then 2i is not an integer. () Prove that equation (*) has a unique solution of period . (b) Prove that if () is false then there exists some b(t) as above such that equation () does not have a -periodic solution