Let $f \colon \Bbb C \to \Bbb C$ be a complex valued function given by $f(z)=u(x,y)+iv(x,y).$ I am stuck on the following question :  
 
MY ATTEMPT:
By Cauchy Riemann equation ,we have $u_x=v_y,u_y=-v_x.$ Now $v(x,y)=3xy^2 \implies v_x=3y^2 \implies -u_y=3y^2 \implies u=-y^3+ \phi(x) $. Now,I am not sure which way to go? Can someone give some explanation about which way to go in order to pick the correct option?

Hint: you used the second C.R. equation arriving at $u(x,y)=-y^3+\phi(x)$. What does it happen if you apply the other C.R. equation, i.e. $u_x=v_y$, to your result?
