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

This question appeared in 65-1,65-2 and 65-3 versions of the paper in 2013.

Given $y=mx$ where $m$ is an arbitrary constant.
Differentiating both sides, we get $\large \frac{dy}{dx}$$=m. Substituting for m =$$\large \frac{dy}{dx}$ in $y=mx$, we get:
$\Rightarrow y=\large \frac{dy}{dx}$$x \rightarrow x\frac{dy}{dx}-y=0.$
edited Mar 21, 2013