On the Linear Differential Equation of Second Order

Abstract

We consider the equation p(x)y''+q(x)y'+r(x)y=0 for p''-q'+r=0, where it is possible to obtain the solutions y1 and y2 of the corresponding homogeneous equation and a particular solution yp for the original equation, and also for p''-q'+r#0, where we must know y1 to construct y2 and yp via two integrations of certain differential relation.