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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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\textit{E. Yaşar}, Math. Probl. Eng. 2011, Article ID 916437, 10 p. (2011; Zbl 1235.70167)

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### References:

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