[SOLVED] Second-Order Linear Non Homogeneous ODE with Constant Coefficients

Here it is:

So the auxiliary/characteristic equation will look like:

Solving that gives:

And so we'll get the following general homogeneous solution:

So now I try to find the particular non homogeneous solution, trying:

Finding the first and second derivative of y particular:

Then, when I try to compile all of this, to then equate coefficients and solve for alpha and beta, I realise that the x terms do not cancel out (as they should) and I cannot go any further (I don't think).

It will eventually look like this:

Have I made an error somewhere?

Any help is appreciated.

NB: It may/may not help, but in the previous part of the question we've already proved that when: