Posted by Jake on Monday, February 28, 2011 at 2:58am.
Note that the right-hand side is homogeneous (i.e. the total of exponents of x and y equals 2 for all terms), so a substitution of u=y/x will render the equation separable.
u=y/x
udx+xdu=dy
dy/dx = u+x*du/dx
...
Post if you have difficulties.