Prove that if A is a linear transformation of Rn and f : Rn → Rn iss a (smooth) function such that |f(x)| ≤ M|x|+N for positive constants M and N, then the differential equation dx/dt = Ax + f(x) has a complete flow.

It was in the Gronwall’s Inequality theorem section.

A is a function of t, ie: A(t). Also A is continuous