Question

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

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}, \\ y=mx.....\left(1\right) \\ \mathrm{Differentiating}\mathrm{with}\mathrm{respect}\mathrm{to}x \\ \Rightarrow \frac{dy}{dx}=m \\ \mathrm{Substituting}\mathrm{the}\mathrm{value}\mathrm{of}m=\frac{dy}{dx}\mathrm{in}\mathrm{eq}\left(1\right)\mathrm{we}\mathrm{get}, \\ y=x\frac{dy}{dx} \\ \mathrm{Hence},y=x\frac{dy}{dx}\mathrm{is}\mathrm{the}\mathrm{required}\mathrm{differential}\mathrm{equation}. \end{gathered}$$