## ABSTRACT

The last several chapters were devoted to solving homogeneous linear differential equations. This rather short chapter provides the transition to the solving of nonhomogeneous linear differential equations, that is, equations of the form a 0 y ( N ) +   a 1 y ( N − 1 ) +   ⋯ +   a N − 1 y ′ + a N y = g https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9780429347429/810905ee-d221-4cf6-8558-ee5123ad5cd2/content/eq3106.tif"/>

where the ak ’s and the g are functions with g not being the zero function. The chapter starts with the derivation of the general form for the general solution to such an equation being the sum of a single particular solution to the given nonhomogeneous differential equation with the general solution to the corresponding homogeneous linear differential equation. A variation on the principle of superposition plays a major role throughout this chapter. It is used in the initial derivations. It also is used near the end of the chapter to show how solutions to the above differential equation can be constructed when the forcing function, g, is a linear combination of simpler functions.