I need to solve this system of differential equations:
$\dot{A}=g_1AC+g_2A^2+g_3C^2$
$\dot{B}=g_1BC+g_2C^2+g_3B^2$
$\dot{C}=\frac{g_1}{2}(AB+C^2)+g_2AC+g_3BC$
Probably I can try to write it in the form of $\dot{X}=X^2$ where $X=aA+bB+cC$ but I'm not quite sure of how to proceed in this way.
Does Mathematica is able to solve that? Or does anyone have any idea of how to handle the system above?
Thank you!