Integrating a path through an acceleration vector field

I think there has been discussion of this but I wonder if there is a workaround. I have a graph which calculates the acceleration a particle would experience depending on x and y coordinates. I’m impressed that it succeeded in this as it is already a double integral over a function that has infinities at the boundary.

What I want to do next is add a particle (or set) with an initial location and velocity and have Desmos work out the subsequent path. The problem of course is that while I could write two integrals to find the velocity then location as a function of time, the acceleration depends on the location and Desmos doesn’t currently support that kind of recursion. Is there any approach to getting round this limitation?