Chapter 4.2, Problem 5P

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.

$(x+3)y"+xy\text{'}+\left(\ln \left|x\right|\right)y=0,y(1)=0,y\text{'}(1)=1$