Chapter 1.2, Problem 16P

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.

$y\left(x\right)=c_1{x}^2\cos \left(3\ln x\right)$, $x^2{y}^{″}-3x{y}^{\prime }+13y=0$.