Form the differential equation representing the family of curves $y=mx$, where $m$ is arbitrary constant.

The correct answer is $\dfrac{dy}{dx}$ = $\dfrac{y}{x}$

$y=mx$

Differentiating with respect to $x$,

$\dfrac{dy}{dx}$ = $m$

Putting this value of $m$ in the above equation,
$y=mx$ ⇒ $y=\dfrac{dy}{dx}x$


∴ $\dfrac{dy}{dx}$ = $\dfrac{y}{x}$