A generalization of d'Alembert formula

In this paper we find a closed form of the solution for the factored inhomogeneous linear equation Pi(n)(j=1) (d/dt - A(j)) u(t) = f(t). Under the hypothesis A(1), A(2),..., A(n) are infinitesimal generators of mutually commuting strongly continuous semigroups of bounded linear operators on a Banach space X. Here we do not assume that A(j)s are distinct and we offer the computational method to get explicit solutions of certain partial differential equations.