In this chapter we consider differential equations of the form y'+p(x)y=q(x) where p(x) and q(x) are given functions of x. Such differential equations are called first order linear. These differential equations are very important for three reasons. First, they are the most understood mathematically—all solutions are explicit, and can always be written as an integral. Second, they occur very often in models and applications. Third, certain other types of differential equations can be reduced to linear differential equations by a change of variable.