I have been given the differential equation $T'(t)=k(T(t)-A)$, where $T$=temperature, $t$=time, $A$=the constant temperature of the surroundings and $k$ is constant.

How do I find $T(t)$ expressed with $T\_o$ = temperature when $t=0$, $A$ and $k$.

It says to use the substitution with $u(t)=T(t)-A$.

Thanks :)