Integrating Factors and First Integrals for Liénard Type and Frequency‐Damped Oscillators

We consider Liénard type and frequency-damped oscillator equations. Integrating factors and the associated first integrals are derived from the method to compute -symmetries and the associated reduction algorithm. The knowledge of a −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