1. Consider the following differential equation for y(m) and F (:13) d2 d +2a+9a2y=F(m) (1) where a is some arbitrary non-zero real constant and y(0) = 3 and y'(0) = a. (a) For which values of a does y(:c) exhibit oscillations? (b) Solve equation (1) where F(:I:) = 0. (c) Solve equation (1) where FCC) = 6". Check that your nal solution indeed satises y(0) = 3 and y'(0) = a. If not, you have made a mistake! (d) Solve equation (1) where F(;r) = 6"" sin(2\/c33 + R), for some real constant R. (e) Part (d) yields more than one particular solution. Is your nal solution to part (d) unique? Discuss briey (no more than 6 lines). There is no need to prove your result