Please take a look at the example at the bottom (at eq. 18:18, at page 619):
Mathematical Methods for Physics and ... - Google Bogsøgning
Q1: In case (ii), why do they add g(x^2+y^2)?
Q2: Why do they not add it in case (i)?
Q3: In case (ii), if I chose f(p) = p + 1 instead of f(p) = 2p, then the solution would be u(x,y) = 1+ x^2 +y^2 + g(x^2 + y^2), right?
I hope you can help me; I find this really hard to understand, and I've spent hours trying to find out, but I find that the book is poorly written. They don't emphasize the important things at all, and the reader is left behind with so many questions.
Thanks in advance.