I have a system of nonlinear differential equations of this kind:
$$f_0\left(\rho(t),\dot\rho(t),\ddot\rho(t),\phi(t),\dot\phi(t),\ddot\phi(t)\right)=0$$ $$f_1\left(\rho(t),\dot\rho(t),\ddot\rho(t),\phi(t),\dot\phi(t),\ddot\phi(t)\right)=0$$ with initial conditions: $$\rho(0)=\rho_0,\phi(0)=\phi_0,\dot\rho(0)=\dot\rho_0,\dot\phi(0)=\dot\phi_0$$
Because is impossible to find a closed form solution, I solved it numerically. Now, I suppose to have the numerical solution. Is it possible to find the initial conditions from the set of numerical data? Thanks