` y^(2)-x^(2) (dy)/(dx) = xy(dy)/(dx)`

y^2+x^2(dy)/(dx)=x y(dy)/(dx)

a(x(dy)/(dx)+2y)=xy(dy)/(dx)

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

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

xy(dy)/(dx)=y+2

The degree of the differential equation : xy((d^(2)y)/(dx^(2)))^(2)+x^(4)((dy)/(dx))^(3)-y(dy)/(dx)=0 is :

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

x^(2)(dy)/(dx) = x^(2) - 2y^(2) + xy