Differential Operator Method of Finding A Particular Solution to An Ordinary Nonhomogeneous Linear Differential Equation with Constant Coefficients

Abstract

We systematically introduce the idea of applying differential operator method to find a particular solution of an ordinary nonhomogeneous linear differential equation with constant coefficients when the nonhomogeneous term is a polynomial function, exponential function, sine function, cosine function or any possible product of these functions. In particular, different from the differential operator method introduced in literature, we propose and highlight utilizing the definition of the inverse of differential operator to determine a particular solution. We suggest that this method should be introduced in textbooks and widely used for determining a particular solution of an ordinary nonhomogeneous linear differential equation with constant coefficients in parallel to the method of undetermined coefficients.