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

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

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

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

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

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

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

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

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

(dy)/(dx)+(xy+y)/(xy+x)=0

The solution of the ( dy )/(dx) = (xy+y)/(xy+x) is :

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