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

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

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(dy)/(dx)=x+xy

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

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) = (2xy)/(x^(2)-1-2y)

General solution of (dy)/(dx)+(2xy)/(1+x^(2))=0 is

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

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

The first integral of (dy)/(dx)((d^(2)y)/(dx^(2)))-x^(2)y((dy)/(dx))=xy^(2) will be