Originally Posted by

**steph3824** Show that the given equation is homogeneous and solve the differential equation.

$\displaystyle dy/dx=x^2+3y^2/2xy

$

To show that it is homogeneous, I have $\displaystyle dy/dx=1+3(y/x)^2/2(y/x)$

I am pretty sure that this is correct so far. Then,

$\displaystyle x(dv/dx)+v=1+3(y/x)^2/2(y/x)$

$\displaystyle x(dv/dx)=1+3(y/x)^2/2(y/x)-v$

$\displaystyle x(dv/dx)=(1+3v^2/2v)-v$

It is after this where I'm not quite sure what to do. According to my book the answer is $\displaystyle x^2+y^2-cx^3=0$. Thanks for any help