For the following initial value problems, give the largest interval where a unique solution is guaranterd to exist ( You do not need to find the solution ) . Briefly justify your answers.
( a ) ( t - 3 ) y ' + ( lnt ) y = 2 t , y ( 1 ) = 0
( b ) ( 9 - t 2 ) y ' + 2ty = 3t 2 , y ( - 4 ) = 6