Question

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

Answer 1

Given that $y=mx$ , where $m$ is arbitrary constant.

Now differentiate the given equation w.r.t $x$, we get

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

Therefore the original equation will become $y=\frac{dy}{dx}x$

$⟹\frac{dy}{dx}=\frac{y}{x}$