The rate of change of the volume, $V$, of water in a tank with respect to time, $t$, is directly proportional to the square root of the volume. Which of the following is a differential equation that describes this relationship.

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Direct variation can be modeled with the equation $y=kx$ for two variables $x$ and $y$.

Since the rate of change of the volume with respect to time $\dfrac{dV}{dt}$ is directly proportional to the square root of the volume $\sqrt{V}$,

$$y=kx$$ $$\boxed{\frac{dV}{dt}=k\sqrt{V}}$$