Consider the differential equation y 0 = t 2 − y 2 (a) Sketch the direction field for this equation. Show the isoclines for m = 0, 1, −1 and whatever other information is needed to give a good idea of how solutions behave. (b) I claim that the solution satisfying the initial condition y(1) = 1/2 also satisfies y(t) > 0 for every t > 1. Is this assertion correct? Justify your answer. (c) I claim that the solution satisfying y(1) = 1/2 also satisfies y(t) > t for some t > 1. Is this assertion correct? Justify your answer.