Chapter 1.2, Problem 49P

For Problems 45–50, verify that the given function is a solution to the given differential equation. In these problems, $c_1$ and $c_2$ are arbitrary constants.

$y\left(x\right)=c_1{e}^x+c_2{e}^{-x}\left(1+2x+2x^2\right)$, $x{y}^{″}-2y^{\prime }+\left(2-x\right)y=0$, $x>0$.