Equating the Solutions of two nonlinear Differential Equation at a Point

Question

I have this two nonlinear second order differential equations.

1. $(y'(t))^2 = V^2/(A-B\cos(y)),\quad y(0)=0$
2. $(g'(t))^2 = (V-(t-X))^2/(A-B\cos(g)),\quad g(Tfin)=XFin.$

then how to find $y(t)$ and $g(t)$?

How do I solve these equations other than using numerical solutions? MATLAB has no analytical solution for these. I need to find $X$ by equating $y(X)=g(X)$. So I need to find $y(t)$ and $g(t)$ analytically to equate them. Then I would solve for $X$ to find it symbolically, that was my plan.

If I choose Runge-Kutta 4th order or any other numerical solution, I don't think I can find $X$ symbolically but I am not sure. Any comment would be appreciated!