Chapter 4.2, Problem 7P

In each of the Problems $1$ through $8$, determine the longest interval in which the given initial value problem is certain to have a unique twice differentiable solution. Do not attempt to find the solution.

$(1-x^2)y"-2xy\text{'}+(\alpha (\alpha +1)+{\mu }^2/(1-x^2))y=0,y(0)=y_0,y\text{'}(0)=y_1$