I have encountered the following system of differential equations in lagrangian mechanics. Can you suggest a numerical method, with relevant links and references on how can I solve it, and the implementation in C (if possible) Also, is there a shorter implementation on Matlab or Mathematica?\begin{align*}mx \dot y^2 + mg\cos(y) - Mg - (m+M)\,\ddot x &= 0 \\g\sin(y) + 2\dot x\dot y + x \,\ddot y &= 0\end{align*}where $\dot x$ or $\dot y$ are time derivatives, and the double dots indicate a 2nd derivative wrt time.
Solving two coupled non-linear second order differential equations numerically
numerics;matlab;mathematica