. Consider the differential equation below, in which a, b, c, k are real constants and c2 + k2 > 0: diy_ ax+by (3\") dm _ cm+ky' 2 (a) Find 4 specic numbers (1,1), 0, k for which the function y : :1: 337 provides a solution for equa- tion (*) on the interval (0, +00). Briey explain your method. (b) Is there only one correct answer to part (a)? If so, explain why; if not, describe the set of all choices for (a, b, c, k) that should be accepted. (0) Consider the ODE (ac) with the constants found in part (a). Find a solution satisfying y(2) = :g. Hint: Start by postulating y : mu(m) for some new unknown function u. Find a, then recover y