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

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

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

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

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

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

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

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

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

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

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

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