On perturbation theory and its application in solving ordinary differential equations using the asymptotic expansion method

Abstract -The perturbation theory is one of the tricks or tools used mathematically to find approximate solutions to fluctuating problems for which no accurate solutions can be found. In this paper we will deal with a number of basic concepts related to perturbation theory, including regular perturbation and singular perturbation, and then apply these tricks or tools theoretically to ordinary first and second order differential equations for regular perturbation using the asymptotic expansion method, which is considered one of the most important methods used to find approximate solutions of perturbation equations.