From Michaelis-Menten kinetics one could easily derive scalar first-order differential equation $$\frac{dx}{dy} = A_0 + A_1 x + A_2 y + B \frac{y}{x},$$ where $A_0, A_1, A_2, B$ are some constants, that depend on rates of reactions.

I'm interested if there are any mathematical facts, that known for this type of equation. I doubt that it is possible to find explicit analytical solution in elementary functions. Also I see that this type of equation doesn't admit nonlinear superposition (unlike Riccati equation, for example).