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

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

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

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

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

Solution of the differential equation xy^(3)(dy)/(dx)=1-x^(2)+y^(2)-x^(2)y^(2) is

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

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

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

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