Problem 3 (Existence and uniqueness). Consider the following initial value problems. Which of them satisfy the hypotheses of the existence and unique- ness theorem for second order equations (and therefore admit a unique solution)? In each case, justify your answer. 1. y" + tzy' + 3/2 = 0 with initial conditions y(0) = 1, y'(0) = 0; 2. y" + tzy' + y2 = 0 with initial condition y(0) = 1, 3. y" + tzy' +yl/2 = 0 with initial conditions y(0) = 1, y'(0) = 0