2022-01-062022-01-062011Yaşar, E. (2011). "Integrating factors and first integrals for Liénard type and frequency-damped oscillators". Mathematical Problems in Engineering, 2011, 1-11.https://www.hindawi.com/journals/mpe/2011/916437/1024-123X1563-5147https://doi.org/10.1155/2011/916437http://hdl.handle.net/11452/23891We 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.eninfo:eu-repo/semantics/openAccessEngineeringMathematicsSymmetriesEquationsLinear systemsOscillators (mechanical)First integralFirst-orderIntegrating factorOscillator equationsReduction algorithmsSystems of partial differential equationsPartial differential equationsArticle0002935823000012-s2.0-800526623211112011Engineering, multidisciplinaryMathematics, interdisciplinary applicationsSecond-order Ordinary Differential Equations; First Integral; Lie Symmetry