On Linearization by Generalized Sundman Transformations of a Class of Li�nard Type Equations and Its Generalization

Abstract

We study the linearization of a class of Li ´ enard type nonlinear second-order ordinary differential equations f rom the generalized Sundman transformation viewpoint. The linearizing generalized Sundman transformation for the class of equations is constructed. The transformation is used to map the underlying class of equations into a linear second-order ordinary differential equation which is not in the Laguerre form. The general solution of this class of equations is obtained by integrating the linearized equation and applying the generalized Sundman transformation. Moreover, we apply a Riccati transformation to a general linear third-order variable coefficients ordinary differential equation to extend the underlying class of equations and we also derive the conditions of linearizability of this new class of nonlinear second-order ordinary differential equ ations using the generalized Sundman transformation method and obtain its general solution.