Question

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

Answer 1

We have,
y = mx (1)
Differentiating both sides, we get
$$\begin{gathered} \frac{dy}{dx}=m \\ \Rightarrow \frac{dy}{dx}=\frac{y}{x}\left[\mathrm{From}\left(1\right)\right] \\ \Rightarrow x\frac{dy}{dx}=y \\ \Rightarrow x\frac{dy}{dx}-y=0 \end{gathered}$$