For realtime simulation it is important to have an ODE solver that is simple enough. I did not find any plug-and-play kind of ODE solvers for realtime applications so I wrote one myself. The greatest benefit of this approach is that you have full control of every time step. Good for realtime simulations.

https://github.com/sebnil/Python-ODE-Forward-Euler/blob/master/Forward-Euler%20ODE%20solver.ipynb

It is very simple but show the basics of how to write an ODE solver. It could be extended to use more sophisticated solvers like Runge-Kutta or Crank-Nicolson.