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" +Py' + y? = 0 with initial conditions y(0) 1, y' (0) = 0; %3D 2. y" + Py' + y? = 0 with initial condition y(0) = 1, 3. y" +ty' +y/2 = 0 with initial conditions y(0) = 1, y'(0) = 0.