2. dy = 2y3(y2 + 2)4((1 − y)9, y(0) = 0.5 dt
(a) Prove the initial value problem has one and only one solution. (Note: You do not need to actually compute the solution).
(b) Prove that this solution satisfies 0 < y(t) < 1 for all t for which it is defined. Include accurate pictures illustrating your reasoning.