Since it is a homogeneous equation, substitute $\displaystyle y=vx$
$\displaystyle \frac{dy}{dx}=v+\frac{dv}{dx}$
Your equation:
$\displaystyle \frac{dy}{dx}=-\frac{3xy}{x^2+y^2}$
substituing y=vx, we get
$\displaystyle v+\frac{dv}{dx}=-\frac{3v}{1+v^2}$
Can you continue from here?