Im doing my Differential Equation's homework, and I've come across some really hard problems, when it got really complicated I tuoght i was wrong (you know book's problems tend to workout nicely) . . .anyways I got REALLY stuck on this one if anyone can guide me thank you 1. The problem statement, all variables and given/known data y''+3y'+2y = 1/(1+ex) 2. Relevant equations Use variation of parameters (the chapter is about wronskians) 3. The attempt at a solution first we find the complementary equation using the auxiliary equation (m2+3m+2) and find that yc=c1e-2x + c2e-x therefore y_1=e^-2x and y_2=e^-x then we use the Wronskian of | y_1 y_2 | | y'_1 y'_2 | = -e^-3x - ( -2e^-3x) therefore W= e^-3x W_1= using f(x) = 1/(1+e^x) | 0 y_2 | | f(x) y'_2 | = 1 / (e^x+e^2x) = u' to find yp=u1y1 + u2y2 the problem is finding u, since the u' = W_1/W . . .which would yield e^3x / (e^x+e^2x) I would have to integrate that, I cant find anyway to do it, I tried integration by parts and partial fraction decomposition. I was thinking of looking it up in an integration table. But since its a problem from the book (and the book doesnt have an integration table) I dont think the book is THAT demanding as in to go look it up in another book. Im thinking maybe im doing something wrong. . . == Thank you!