A. R. Vahidi - Department of Mathematics, College of Science,Yadegar-e-Imam Khomeini (RAH) Shahr-e-Rey ‎Branch, Islamic Azad University, Tehran, Iran.
Z. Azimzadeh - Department of Mathematics, College of Science,Yadegar-e-Imam Khomeini (RAH) Shahr-e-Rey ‎Branch, Islamic Azad University, Tehran, Iran.
M. Shahrestani‎ - Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, ‎Iran.‎

In this paper a new form of the homptopy perturbation method is used for solving oscillator differential equation, which yields the Maclaurin series of the exact solution. Nonlinear vibration problems and differential equation oscillations have crucial importance in all areas of science and engineering. These equations equip a significant mathematical model for dynamical systems. The accuracy of the Solution equation is very important because the analysis component of the system like vibration amplitude control, synchronization dynamics are dependent to the exact solution of oscillation ‎equation.

Homotopy perturbation method (HPM)‎, ‎ Differential equations, Non-linear oscillator's equation, Laplace ‎transformation