SECTION 6 - Solutions of Linear Equations

Abstract

This chapter discusses the solution of linear equations with constant coefficients. It describes the nature of the general solution of linear homogeneous equations. There is a method of finding the solutions of homogeneous linear differential equations with constant coefficients. In addition, by the method of variation of the coefficients, one can find a particular solution of a nonhomogeneous equation with the help of the general solution yh of the homogeneous equation. In practice, however, this method is somewhat complicated. The chapter describes the operators method that simplifies this task in most cases. There are two additional methods that are conveniently used to obtain particular solutions of a restricted class of differential equations, namely, the method of infinite expansions of L(D) and the Laplace transform.