By the way, although it wasn't asked, if T< , so T increases to . dT/dt is positive now which means that, since T- is negative, k must still be negative. The "k" in Newton's law of cooling is always negative.
"Separate" it: . Integrate both sides. You will get a logarithm on the left so solving for T will give an exponential of kt.Find the GS of the DE . You may assume and the final solution should give explicitly in terms of and a constant of integration.
Could someone give me a helping hand with this? I'm new to differential equations and this question was just thrown at me unexpectedly.