Integrability Analysis of a Generalized Truly Nonlinear Oscillator Equation

The integrability of a general class of Lienard type equations is investigated through equation transformation theory. In this way it is shown that such a class of Lienard equations can generate a generalization of some interesting truly nonlinear oscillator equations like the cube and fifth root differential equations. It has then become possible to compute the exact and general solution to the generalized truly nonlinear oscillator equation. Under an appropriate choice of initial conditions, exact and explicit solution has been obtained in terms of Jacobi elliptic functions.