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RE: Mathematics - Linear second-order Differential equations with constant coefficients
Great! It's refreshing to read posts like this that stand out from most others.
What is actually, if R (x) is a power series? If R (x) does not fall into any of the cases you deal with, it would have to be represented as a power series.
There are of course more R(x) cases, but these are the "simplest".
If R(x) doesn't fall into any of the cases then we find yp (solution of the given ODE) with the Lagrange method.
Using a specific equation we can get yp using y1, y2 and the Wronsky determinant.
More about that in a sec, I am writing the post for today at the moment! :)