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(B) Given the family of curves: $y = mx$  ............$(1)$Differentiating both sides of equation $(1)$ with respect to $x$,we get:$\frac{dy}{dx} = m$

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$x \frac{dy}{dx} - y = 0$

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(B) Given the family of curves: $y = mx$  ............$(1)$Differentiating both sides of equation $(1)$ with respect to $x$,we get:$\frac{dy}{dx} = m$Substituting the value of $m$ from this derivative into equation $(1)$,we get:$y = (\frac{dy}{dx}) \cdot x$Rearranging the terms,we obtain:$x \frac{dy}{dx} - y = 0$This equation is free from the arbitrary constant $m$,and therefore,it is the required differential equation.

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

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