Question

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

Answer 1

it is as shown in the attachment

Step-by-step explanation:

The detailed and mathematical step by step explanation is as shown in the attachment.

The general solution x(t) = KAo/K² + w² [kcoswt + wsinwt] + Cexp(-kt)