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" 6."quad (x^(2)+2xy+y^(2)+1)(dy)/(dx)=2...

" 6."quad (x^(2)+2xy+y^(2)+1)(dy)/(dx)=2(x+y)

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

Solve: (x^2+2xy+y^2+1)(dy)/(dx)=2(x+y)

Solve: (x^2+2xy+y^2+1)(dy)/(dx)=2(x+y)

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

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

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

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

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

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

(1+x+xy^(2))(dy)/(dx)+(y+y^(3))=0