Problem goes as follows :

(y^2 + x^2)dx + (2xy)dy = 0

Now I can clearly see it is homogeneous but my problem starts once I get it in derivative form. Once in derivative form, I subbed u = y/x , y = ux , dy/dx = (du/dx) x + u.

Once I subbed it all in, I was left with

u + du/dx = - (1 + u^2) / (2u)

Can someone help me proceed from here?