Help Finding Explicit Solution Non Linear Differential Equation

Hello!

I am wondering if anyone has any advice to try to find an explicit solution (or some approximation) for the following non-linear differential equation system:

Is there any method to try to arrange these equations to find an explicit solution? Or define some constrains in the solver to find a solution for some restricted domain?

I know the constants real and positive and the region of interest is x and y > 0 (same for initial conditions).

By using some numerical values, I found the solutions look like some kind of spiral. I would like to have some way to characterize these curves (like the position of the center, radius, etc...) and how A,B,C and D, somehow modifies the shape of the solutions.

Any help, hint or advive is greatly appreciated!

Thanks!