The question:

My attempt:

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 .

Finding derivatives:

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!