Lol?
e^ax(a^2+2a+1) = 0
e^ax =/= 0 so thus a^2+2a+1 = 0.
And lol, of course you need a simple guess, you solve the homogenous equation and if the RHS of the ODE is a function g(x) then you guess the most general solution to g(x).
If you haven't done ODE's before then I'd advise you to be quiet.