Non-linear system of 2 equal differential equations

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I am trying to solve a nonlinear system of differential equations:

$a\ddot{x} = -\frac{b}{\sqrt{\dot{x}^2 + \dot{y}^2}}\dot{x}$

$a\ddot{y} = -\frac{b}{\sqrt{\dot{x}^2 + \dot{y}^2}}\dot{y}$

The fact that both equations for $x$ and $y$ are the same makes me think that I may be able to find an analytical solution for this system. For now, I have tried with different combinations of sines and cosines, with low success.

Any ideas are well appreciated!