The structure of (while looking quite random and complex at first) actually yields some good clues:

Start with the original function:

Rewrite:

Denote new functions and

The equation now becomes:

Deriving, , or

Therefore ------(1) (The same result can be shown using Taylor Series)

Find such an A and B and convert them back in terms of f and g: and

I have looked at a handful of candidate functions, A and B but have not found anything by trial.Find any two functions A and B whose sum equals the ratio of their first derivatives or prove that none exist.This is just a first order differential equation, so it should be possible to solve. I took the liberty of starting a thread for the DiffEq guys to look into it: http://www.mathhelpforum.com/math-he...96754-b-b.html