Finding homogeneous solution:
So we have
Finding a particular solution, I tried , but noticed that this is also a solution to the homogeneous equation. So instead, I went with .
Substituting into the ODE:
Clearly a = -1, so:
So we want
Substituting into the general solution:
Adding homogeneous and particular solutions:
However, the solution is:
I'm not sure where that x came from. I'm sure I'm missing something obvious here. Any help would be great!