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In a two-dimensional steady flow field, in a certain region of the $x-y$ plane, the velocity component in the $x$-direction is given by $v_x=x^2$ and the density varies as $\rho = \dfrac{1}{x}$. Which of the following is a valid expression for the velocity component in the $y$ – direction, $v_y$?

- $v_y= \:– x/y$
- $v_y = x/y$
- $v_y = \:-xy$
- $v_y = xy$