Find the particular solution to

First, I found that the general solution is

So the list of terms that I obtain here is:

Now, for my guess of the particular solution, I have list of terms

Since I have repeats, I would take the derivative, so I have new list

So my particular solution is:

I know I'm missing something, I think I'm suppose to multiply x by one of the list, but I just can't remember what the method was, please help. Thanks.