Factorization method for some inhomogeneous Liénard equations

We obtain closed-form solutions of several inhomogeneous Li´enard equations by the factorization method. The two factorization conditions involved in the method are turned into a system of first-order differential equations containing the forcing term. In this way, one can find the forcing terms that lead to integrable cases. Because of the reduction of order feature of factorization, the solutions are simultaneously solutions of first-order differential equations with polynomial nonlinearities. The illustrative examples of Li´enard solutions obtained in this way generically have rational parts, and consequently display singularities.