Integrating factors and first integrals for Liénard type and frequency-damped oscillators

Abstract

We consider Lienard type and frequency-damped oscillator equations. Integrating factors and the associated first integrals are derived from the method to compute lambda-symmetries and the associated reduction algorithm. The knowledge of a lambda-symmetry of the equation permits the determination of an integrating factor or a first integral by means of coupled first-order linear systems of partial differential equations. We will compare our results with those gained by the other methods.