For each initial value problem, determine the largest ( t )-interval on which Theorem 3.1 guarantees the existence of a unique solution. ( ty''+sin(2t)/t²-9y'+2y=0, , y(1)=0, , y'(1)=1 ):
a) ( (-[infinity], -3) )
b) ( (-[infinity], -3) ∪ (-3, 3) )
c) ( (-3, 3) )
d) ( (-3, [infinity]) )