A set couple ODE's

Question

$$\frac{d^2x}{{\rm dt}^2}=-GM\frac{x}{{(x^2+y^2)}^\frac{3}{2}}$$

$$\frac{d^2y}{{\rm dt}^2}=-GM\frac{y}{{(x^2+y^2)}^\frac{3}{2}}$$

How can I solve those equations, I tried using wolfram alpha but it didn't work.

Answer 1

These are the equations for a body in a gravitational field. The solution is obtained via the Kepler laws.