Chapter 4.1, Problem 34E

In Problems 31–34 verify that the given two-parameter family of functions is the general solution of the nonhomogeneous differential equation on the indicated interval.

33. $\begin{array}{l}2x^{2}y"+5xy\text{'}+y=x^2-x;\hfill \\ y=c_1{x}^{-1/2}+c_2{x}^{-1}+\frac{1}{15}{x}^2-\frac{1}{6}x,(0,\infty )\hfill \end{array}$