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

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

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

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

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

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

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

y The differential equation of all circles passing through the origin and having their centres on the x-axis is (1)x^(2)=y^(2)+xy(dy)/(dx) (2) x^(2)=y^(2)+3xy(dy)/(dx)y^(2)=x^(2)+3xy(dy)/(dx)y^(2)=x^(2)-2xy(dy)/(dx)

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