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

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

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

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

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

x^(2)dy+(x^(2)-xy+y^(2))dx=0

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

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

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

Express (x sqrt(x^(2)+y^(2))-y^(2))dx+xy dy=0 in the form (dy)/(dx)=F((y)/(x)) .