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Integrating factors and first integrals for Liénard type and frequency-damped oscillators. (English) Zbl 1235.70167

Summary: We consider Liénard 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.

MSC:

70K99 Nonlinear dynamics in mechanics
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
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