Find the general solution for y' +3y = t + e^(-2t) for y.
The Attempt at a Solution
At first I thought that since the equation was already separated, I could simply integrate both sides and get a solution easily:
That results in 1.5 y^2 + y = .5t^2 - .5e^(-2t)
(Unless I made a simple error, which is quite possible.)
However, I quickly realized that this is not the approach to take, since it still contains multiple powers of y.
So, I suspect that I will need to find an integrating factor to multiply by, (commonly called mu, I believe) but I'm not sure how you're supposed to find that.