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

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

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

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

The solution of (x^(2)+xy)dy=(x^(2)+y^(2))dx is

The solution of (x^(2)+xy)dy=(x^(2)+y^(2))dx is

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

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

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