I'm trying to solve the following ODE:


where the functions $P(x)$ and $Q(x)$ are known.

This nearly resembles Abel Equation of first kind. The power in $f$'s is of 1 order too high. Maybe this equation has a 'canonical form' like in Abel equation of the first kind.

Any hints on solving this? Maybe someone sees a way to reduce it to one of the forms in List of nonlinear ODE


Equivalently, for $f(x)=\frac{1}{g(x)}$:



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