(dy)/(dx)(x^(2)y^(3)+xy)=1

(dy)/(dx)=x^(3)y^(3)-xy

The solution of the differential equation x=1+xy(dy)/(dx)+(x^(2)y^(2))/(2!)((dy)/(dx))^(2)+(x^(3)y^(3))/(3!)((dy)/(dx))^(3)+...is

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

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

(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)

"If "y=sqrt(x+sqrt(y+sqrt(x+sqrt(y+...oo))))," then prove that "(dy)/(dx)=(y^(2)-x)/(2y^(3)-2xy-1)