An analysis of the nonlinearizable classes of Emden-Liénard equations

Abstract We present a general method to construct first integrals for some classes of the well known second-order ordinary differential equations, viz., the Emden and Liénard classes of equations. The approach does not require a knowledge of a Lagrangian but, rather, uses the ‘multiplier approach’ [1, 2]. It is then shown how a study of the invariance properties and conservation laws are used to ‘twice’ reduce the equations to solutions. In this paper, we restrict our work to the nonlinearizable cases.