Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 916437, 10 pages
http://dx.doi.org/10.1155/2011/916437
Research Article

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

Emrullah Yaşar

Department of Mathematics, Faculty of Arts and Sciences, Uludag University, 16059 Bursa, Turkey

Received 25 January 2011; Revised 11 April 2011; Accepted 12 April 2011

Academic Editor: Alexei Mailybaev

Copyright © 2011 Emrullah Yaşar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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