`(dy)/(dx)=x^(3)-2xy`

If the solution of the differential equation (dy)/(dx)=(x^(3)+xy^(2))/(y^(3)-yx^(2)) is y^(k)-x^(k)=2x^(2)y^(2)+lambda (where, lambda is an arbitrary constant), then the value of k is

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

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

(dy)/(dx)=x+xy

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

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

Solution of xy-(dy)/(dx)=y^(3)e^(-x^(2)) is

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

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