In Chapters 1 and 2 we investigated first-order differential equations. We now turn to equations of higher order beginning in this chapter with equations that are linear. The general theory of linear differential equations parallels the second-order case (), which we outline in this initial section.
Recall that a second-order differential equation in the (unknown) function y(x) is one of the form
This differential equation is said to be linear provided that G is linear in the dependent variable y and its derivatives and Thus a linear second-order equation takes (or can be written in) the form