1. In this problem wc will find all functions f (t) which satisfy thc equation f' (t) tf(t). (a) (b) (c) (d) First, show that ct2/2 is such a function. Consider g(t) = Show that if f' (t) = t f (t), then g'(t) = O. Conclude that f(t) = Cct2/2 for some constant C. (You don't need to hand this in.) Think about how you would modify this method to find those functions f(t) which satisfy f' (t) = cos(t)f(t).