Newton's law of cooling states that d x d t = − 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 = a 0 cos ( ω t ) for some constants a 0 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?