I am trying to solve this differential equation. y'' + 3y' + 2y = \frac{1}{e^{x} + 1}
I know that I have to solve $x^2+3x+2=0$
when the solutions of this equation are $(x_1,x_2) = (-2,-1)$
so $y_0(x) = c_1 e^{-2x}+c_2e^{-x}$
Then I am looking for a solution of $y(x) = K \frac{1}{e^x +1}$ and I calculate y' and y''.
The problem is that I end up to nowhere. Can someone help me?