In the previous chapters, we studied one family of methods to solve linear ordinary differential equations. In the current chapter, we make a quick tour of the alternative, namely the Laplace transform method, which attacks the problem in a different paradigm and, in fact, specializes in a certain class of problems which have high practical utility. This also becomes our first encounter with integral transforms, more of which will come later.
In the previous chapters, it was always assumed that the entire differential equation is known in advance, and we go for a complete solution first. Afterwards, as the initial (or other) conditions are supplied, a particular solution can be identified by evaluating the arbitrary ...