The Solution of Weakly Nonlinear Oscillatory Problems with No Damping Using MAPLE

Weakly nonlinear oscillatory problems in engineering dynamics are frequently presented by nonlinear ordinary differential equations. Very few of such equations have exact solutions, thus the need for approximation techniques. In this study, the classical perturbation method, namely the Lindstedt-Poincare method (L-P method) is discussed. In most work, the L-P method is used to obtain uniformly valid approximate solutions to second order only, as perturbation procedure usually involves cumbersome algebraic manipulations and calculations which are time-consuming and prone to errors. Therefore, in this paper we manage to get the solution to fifth order by using our own built in Maple package based on Maple 14 and we include the graphical presentations of the results.