Reduction of order as a neglected method for the solution of inhomogeneous linear ordinary differential equations

Abstract

This paper shows that the method of ‘reduction of order’ is both a simpler way of teaching and of obtaining solutions for inhomogeneous linear ordinary differential equations than is the normally espoused method of ‘variation of parameters’. Details are given of the results of the method for the general nth order equation and the two methods are compared for n = 2, 3. It will be noted that the proposed method takes a particularly simple form when the right‐hand side of the equation is a multiple of one of the solutions to the related homogeneous equation.