Determine the longest interval in which the given initial value problem is certain to have a unique twice-differentiable solution for y′′(cos(t))y′+3(ln∣t∣)y=0, y(2)=3, y′(2)=1.
a) t∈(0,[infinity])
b) t∈(−[infinity],0)
c) t∈(0,2)
d) t∈(2,[infinity])