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

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

The solution to the differential equation (dy)/(dx)=((x+y+1)^(2))/(xy-y+2x-2) is

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

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

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

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

Solution of the differentiable equation x=1+xy((dy)/(dx))+((xy)^(2))/(2!)((dy)/(dx))^(2)+((xy)^(3))/(3!)((dy)/(dx))^(3)+

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

The solution of (dy)/(dx)=(x^(2)+y^(2)+1)/(2xy) satisfying y(1)=1 is given by