1. ## Please help me to find the solutions to this differential equation

2. Since it is a homogeneous equation, substitute $\displaystyle y=vx$

$\displaystyle \frac{dy}{dx}=v+\frac{dv}{dx}$

$\displaystyle \frac{dy}{dx}=-\frac{3xy}{x^2+y^2}$

substituing y=vx, we get

$\displaystyle v+\frac{dv}{dx}=-\frac{3v}{1+v^2}$

Can you continue from here?

4. Originally Posted by redfox2600
It is now of variables separable type, and so routine to solve for v(x).

CB