In this Chapter, we study a particularly important class of second order equations. Because of their many applications in science and engineering, second order differential equation have historically been the most thoroughly studied class of differential equations. Research on the theory of second order differential equations continues to the present day. This chapter is devoted to second order equations that can be written in the form $$P_0(x)y''+P_1(x)y'+P_2(x)y=F(x). \nonumber$$ Such equations are said to be linear. As in the case of first order linear equations, this differential equation is said to be homogeneous if $$F\equiv0$$, or nonhomogeneous if $$F \not \equiv 0$$.