Consider the ODE: 5'0 2 1 + .7310. (A) Let the initial condition be given by 110(0) : a E R. Show that 32(75) 2 1, Vt 2 to, where to = max{1 a, 0}. (B) Show that 9': Z 1 + $2, V152 to. (C) Use (A) and (B) to show that there must be a nite time at which 50(t) blows up. [Hint: integrate the inequality 9?: 2 1 + 3:2 between to and t by separation of variables as you would if it were an equality] (D) Give an estimation of the time of blow up in case a = 1