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

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

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

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

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

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

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

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

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

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