Solving nonlinear differential equations of Vanderpol, Rayleigh and Duffing by AGM

In the present paper, three complicated nonlinear differential equations in the field of vibration, which are Vanderpol, Rayleigh and Duffing equations, have been analyzed and solved completely by Algebraic Method (AGM). Investigating this kind of equations is a very hard task to do and the obtained solution is not accurate and reliable. This issue will be emerged after comparing the achieved solutions by numerical method (Runge-Kutte 4th). Based on the comparisons which have been made between the gained solutions by AGM and numerical method, it is possible to indicate that AGM can be successfully applied for various differential equations particularly for difficult ones. The results reveal that this method is not only very effective and simple, but also reliable, and can be applied for other complicated nonlinear problems.