Given the equation $y''(t) -y'(t) -2y(t) = 3e^{-t} $
Trying to find the particular solution i end up with a $0$ on the left hand side: $$ Ae^{-x} + Ae^{-x} -2Ae^{-x} = 3e^{-x}$$ So that leads me to believe the solution is simply $C_1 e^{-x} +C_2 e^{2x}$ Am I correct or is there something I've missed?
Hint: Make for the particular solution the ansatz $$y_p=e^{-t}(At+B)$$