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: