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!