Parametric factorization of non linear second order differential equations

In this paper the factorization method introduced by Rosu \& Cornejo-P\'erez for second order non linear differential equations is generalized by adding a parameter in order to obtain the general solutions for the mixed quadratic and linear Li\'enard type equation. The new parametric factorization is used to obtain complete analytic solutions for nonlinear second order differential equations. The parametric factorization introduced in this article reduces to the standard factorization scheme when the parameter goes to zero. As an example, we apply the parametric factorization approach to solve the generalized Fisher equation and the Israel-Stewart cosmological model. The parametric factorization presented in this paper can be used in other non linear mixed Li\'enard type equations.