Find the general solution of the given differential equation, and use it to determine how
solutions behave as t→∞.
a) y' − 2y = t2e2t
The Attempt at a Solution
After doing the linear DE steps I end up getting y(t)= t3e2t/3 + ce2t. Now I have a problem in getting the limit. The book says the 'It is
evident that all solutions increase at an exponential rate.' Now, my doubt is how would it increase. Or what makes us sure that it will increase? The first part indeed goes to infinity but the second part has a c which can either be positive or negative. So we can end up getting infinity - infinity. Can someone help me?