The function $f(z)$ of complex variable $z=x+iy$, where $i=\sqrt{-1}$, is given as $f(z)=(x^3-3xy^2)+i \: v(x,y)$. For this function to be analytic, $v(x,y)$ should be

- $(3xy^2-y^3) +$ constant
- $(3x^2y^2-y^3) +$ constant
- $(x^3-3x^2 y) +$ constant
- $(3x^2y-y^3) +$ constant