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" 6."2xy(dy)/(dx)=x^(2)+y^(2)...

" 6."2xy(dy)/(dx)=x^(2)+y^(2)

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

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

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^2y+y)/(xy^2+x)

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