Second- and Higher Order Differential Equations

Consider the second-order linear differential equation \(p_0(t)y''+p_1(t)y'+p_2(t)y~=~r(t),\) where the functions \(p_0,p_1,p_2\), and r are continuous in an open interval \(I=(\alpha ,\beta ),\) and \(p_0(t)\ne 0\) for all \(t\in I\) [1, 2]. For (3.1) the corresponding homogeneous differential equation \(p_0(t)y''+p_1(t)y'+p_2(t)y~=~0\) plays an important role.