It seems to be the case that fundamental matrices are only used when the particular solution has an initial value of 0. Since the integral for the inhomogenous term is from (t. to t) where t. is initial value. So when t=t. the inhomogenous term must be 0. But there are cases when the particlular solution may not have an intitial value of 0 which means those situations cannot be dealt with by Fundamental matrices method of solving ODEs. But I always had the impression that they could solve any systems of ODEs.