Newton’s law of cooling states that dx dt = (x a) where x is the temperature, t is time, a is the ambient temperature, and k > 0 is a constant. suppose that a = a0 cos(! t) for some constants a0 and ! . that is, the ambient temperature oscillates (for example night and day temperatures). a) find the general solution. b) in the long term, will the initial conditions make much of a di erence? why or why not?