While we already have techniques for solving all orders of nonhomogeneous linear differential equations with constant coefficients, those techniques are cumbersome for discontinuous or periodic forcing functions. A method that easily handles these situations by using Laplace transforms will be introduced in this chapter. It provides an alternative method for solving the differential equations in previous chapters by reducing the problem of solving a differential equation to a purely algebraic one. It is particularly suited to initial value problems. This transform method also applies to systems of linear differential equations with constant coefficients.
Because the existence of a table of transforms and inverse transforms of many functions greatly eases the use of Laplace transforms, we develop results that help establish such tables.
Laplace transforms are the method of choice for solving differential equations in some disciplines.