Chapter 1.2, Problem 20P

For Problems 7–21, verify that the given function is a solution to the given differential equation ( $c_1$ and $c_2$ are arbitrary constants), and state the maximum interval over which the solution is valid.

$y\left(x\right)=e^{ax}\left(c_1+c_{2}x\right)$, $y^{″}-2a{y}^{\prime }+a^{2}y=0$, where $a$ is a constant.