First Order Uniform Solution for General Perturbed Harmonic Oscillator

Abstract

In this paper, first order uniform solutions with respect to small parameter  are established analytically for general perturbed harmonic oscillator of the form, 

 

are nonnegative integers. Comparison between these analytical solutions and the numerical solutions of the differential equations is also given for different n, m, and, and showed excellent agreement. A result that confirming the validity of our analytical solutions.