Chapter 4.2, Problem 4P

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.

$y"+(\cos t)y\text{'}+3\left(\ln \left|t\right|\right)y=0,y(2)=3,y\text{'}(2)=1$