Non linear ordinary differential system

Question

Is there an analytical solution (in the general case) to the following differential system (Cauchy Problem) :

$\dot{f}=\frac{Af}{(f^2+g^2)^{1/2}}$

$\dot{g}=\frac{Bg}{(f^2+g^2)^{1/2}}$

with the initial conditions $f(0)=f_0$ and $g(0)=g_0$

Thank you.