Applied Mathematical Sciences, Vol. 11, 2017, no. 34, 1673 - 1686 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ams.2017.74136 Solving Inhomogeneous Nonlinear Differential Equations in Terms of Orthogonal Functions Using the Adomian Decomposition Functions Abdalla Obeidat Physics Department Jordan University of Science and Technology, Jordan Adnan Jaradat Physics Department Jordan University of Science and Technology, Jordan Reham Almomani Physics Department Jordan University of Science and Technology, Jordan Mohammad-Khair Qaseer Physics Department Jordan University of Science and Technology, Jordan Copyright © 2017 Abdalla Obeidat et al. This article is 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 The Adomian decomposition method has been widely used to solve ordinary and partial differential equations. The inhomogeneous term or the source term has been expanded in terms of orthogonal polynomials. In this work we expand the source term in terms of Legendre polynomials, Chebyshev polynomials and Taylor expansion. Our results show that the absolute error is the least when using Taylor expansion.