Chapter 4.2, Problem 6P

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.

$(x-2)y"+y\text{'}+(x-2)(\tan x)y=0,y(3)=1,y\text{'}(3)=2$