Chapter 4.2, Problem 34P

In each of problem 28 through 38, use method of reduction of order to find a second solution $y$ of the given differential equation such that $\{y_1,y_2\}$ is a fundamental set of solution on the given interval.

$\left(x-1\right)y^{″}-x{y}^{\prime }+y=0$; $x>1$; $y_1\left(x\right)=e^x$