Chapter 4.2, Problem 24P

In each of problem 22 through 25, verify that the functions $y_1$ and $y_2$ are the solutions of the given differential equation. Do they constitute a fundamental set of solutions?

$x^{2}y\text{'}\text{'}-x\left(x+2\right)y^{\prime }+\left(x+2\right)y=0,\text{where }x>0$;

$y_1\left(x\right)=x$, $y_2\left(x\right)=x{e}^x$