Differential Equations - Newton's Law of Cooling/Warming?

Question

a)Solve the differential equation:
dT(t)/dt=k(T-tsubm)
k is a constant
T(t) is the temp of object for t>0
Tsubm is the ambient temperature
T subm iss constant

b) T(0) =T sub 0

Please help!

More answers please!!!!!

Answer 1

dT/k(T-tm)= dt
1/k* lnIT-tmI= t+ c
(T-tm)^1/k=Ce^t
(Tsub0-tm)^1/k =C so the solution is
(T-tsubm)^1/k= (Tsub0-tsubm)^1/k * e^t

T= tsubm +(Tsub0-tsubm) *e^kt