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

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

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

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

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

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

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

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

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