This ODE is extremely unlikely to have an explicit solution. Mathematica cannot do anything with this ODE even when $g(x)\equiv x$.
Here is an image of the corresponding Mathematica notebook:
And here is a link to the Mathematica notebook itself.
This ODE is extremely unlikely to have an explicit solution. Mathematica cannot do anything with this ODE even when $g(x)\equiv x$.
Here is an image of the corresponding Mathematica notebook:
And here is a link to the Mathematica notebook itself.