I am trying to get the particular solution to the equation -
$y''' + 4y'' + 5y' + 2y = e^{-t} $
We are taught the method of undetermined coefficients to solve such equations. However, one of the solutions of the homogenous equation is of the form of the particular equation (so when I substitute it, I get LHS$ = 0$, while RHS is not $0$ ).
Please give me a hint on how should I proceed to get the particular solution.
[This question is a part of the tricky questions set given to us. The actual differential equation is a bit more complicated, but I have reduced it to the point I have got stuck in.]