Suppose $u(x,y)$ is a function of $x$ and $y$. Select all solutions of $u_x = 3$. There may be more than one correct answer.

A. $u = 3 y$

B. $u = 0$

C. $u = \sin(3 x)$

D. $u = 3 x + g(y)$ for an arbitrary $g(y)$

E. $u = 3 y + g(x)$ for an arbitrary $g(x)$

F. $u = 3 x$

G. $u = \sin(y) + 3 x$

H. $u = g(3 y)$ for an arbitrary $g(y)$

I. $u = e^y + 3 x$

J. None of the above