Question

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

Answer 1

Given $y=mx$ where $m$ is an arbitrary constant.

Differentiating both sides, we get

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

Substituting for $\frac{dy}{dx}=m$ in $y=mx$ as shown below:

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

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

Hence the differential equation is $x\frac{dy}{dx}-y=0$.