Newton’s law of cooling states that dx dt = −k(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(ωt) for some constants a0 and ω. 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 difference? why or why not?