I am trying to solve an ODE which has the following form: $$ \dfrac{\mathrm{d}y}{\mathrm{d}x} = \frac{Axy \ + \ By^2 \ + \ Cy}{Dxy \ + Ey \ +\ Fx \ + G}$$ with an initial condition $y(x_0) = y_0 \\ $.

The approaches I could think of to solve this equation were to

- Approximate it to a Darboux equation, but the approximations are not desirable.
- Write $x = \dfrac{x}{z}$ and $y = \dfrac{y}{z} $ to get homogeneous degree on the right side, but I am unable to progress further.

Are there any methods to find explicit closed form solutions for such equations?