Using Undetermined Coefficients to Solve Some Classes of Ordinary Differential Equations with Variable Coefficients

Abstract

In most undergraduate differential equations textbooks, there are two methods of finding a particular solution for higher-order nonhomogeneous ordinary differential equations that be introduced. The first one is the method of undetermined coefficients. This method can be used to solving differential equations with constant coefficients but it is limited to cases of a right-hand side function. The second one is the method of variation of parameters, which is not limited to cases of a right-hand side function, nor is it limited to differential equations with constant coefficients but it takes longer time and has more processes than the first one. In this paper, we introduce the method of undetermined coefficients to solve some classes of ordinary differential equations with variable coefficients.