On the General Solutions of a Nonlinear Pseudo-Oscillator Equation and Related Quadratic Lienard Systems

Abstract

We compute explicitly the exact and general solutions of the so-called pseudo-oscillator equation xx ̈+1=0, and of its related quadratic Lienard type equations in a straightforward and direct method. This is achieved using the generalized Sundman transformation theory introduced recently in the literature by some authors of this work.