This is now first-order linear, so you can use the Integrating Factor method to solve...
A global warming model leads to the following equation for the average temperature of the
Earth's surface:
dT/dt = k_{1}exp(k_{2}t) - k_{3}(T-T_{0});
where k1, k2, k3 are positive constants. Determine T(t), assuming that T(1) = T_{0}.
Any assistance would be appreciated (:
My lecturer did not explain how to solve these equations very well and I have tried searching all over the internet for help on solving these equations but I have been unsuccessful and/or lead to more confusion.