Cant solve diff-eq with substitution

Use subs $$y=xv$$ to show that $$(x^2+y^2)+2xy\frac{dy}{dx}=0, x>0$$ is $$x^3+3xy^2=k$$ where k is a constant.

I played around with this at school and if memory serves me correct i got something similar to $$\frac{dx}{dv}=\frac{-3}{2xv}-\frac{1}{2}$$ and after that i decided i wasnt on the right path and stopped. Need a little help here !

 PhysOrg.com science news on PhysOrg.com >> Heat-related deaths in Manhattan projected to rise>> Dire outlook despite global warming 'pause': study>> Sea level influenced tropical climate during the last ice age
 Recognitions: Gold Member Homework Help Science Advisor x is to remain the independent variable; v(x) is the dependent variable which replaces y(x)
 What is v? Is v a function or a constant??

Recognitions:
Gold Member
Homework Help
$$v(x)=\frac{y(x)}{x}$$