Chapter 4.2, Problem 25P

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?

$\left(1-x\cot x\right)y^{″}-x{y}^{\prime }+y=0,0<x<\pi$;

$y_1\left(x\right)=x$, $y_2\left(x\right)=\sin x$