I'm a bit confused as to what I do next with this problem.
Consider the initial value problem \frac{dy}{dx} = a(y-b) where y(0) = y0
With a > 0, b = 0, it represents exponential growth, while a < 0, b = 0 gives exponential decay. With y = T, a = -k, k = TA and y0=T0 it gives Newton's Law of...