Quote:

Find the GS of the DE $\displaystyle \frac{dT}{dt}=k(T-T_{a})$. You may assume $\displaystyle T-T_{a} > 0$ and the final solution should give $\displaystyle T$ explicitly in terms of $\displaystyle k, t, T_{a}$ 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.

"Separate" it: $\displaystyle \frac{dT}{T- T_a}= kdt$. Integrate both sides. You will get a logarithm on the left so solving for T will give an exponential of kt.