Some ideas?

A6*x + A4*(y')^2 - 2*A2*x'' - A3*x*y'' + A4*y*y'' = 0

A5 - A3*(x')^2 - A3*x*x'' + A4*y*x'' - 2*A1*y'' = 0

'=(d/dt), ''=(d^2/dt^2), Ai-known constants. The initial conditions are:

x(0)=a, y(0)=0, x'(0)=0, y'(0)=0.

Thank you in advance!!!