In the previous chapter we developed solutions of homogeneous second order linear differential equations with constant coefficients. Because many important applications of differential equations deal with nonhomogeneous linear differential equations—those with forcing functions—we consider that situation in this chapter.

We will discover a straightforward technique that always works for a very restricted, but important, class of forcing functions. We introduce a technique—the Principle of Linear Superposition—that allows us to construct new solutions from old ones. Mathematical models of forced spring-mass systems and electrical circuits are among the applications considered.