Problem #1: Consider the following differential equation, (x2 - 16) y'" + sin(2x)y' = In(1+6x2) cos(x2 )y What is the largest interval for which Theorem 2 implies a unique solution to the differential equation with the following conditions? If your interval is (a, b), then enter the values of a and b (in that order) into the answer box, separated with a comma. (Use infinity for wo, if needed.) If Theorem 2 does not provide an interval, then enter DNE, ONE (a) y(1) = 2, y'(1) = 2. (b) y (-1) = 2, >' (-2) = 3 (c) y( -8) = 2, y'(-8) =4 Enter your answer Problem # 1(a): symbolically, as in these examples Enter your answer. Problem # 1(b): symbolically, as in these examples Enter your answer Problem #1(c) : symbolically as in the