Question

Write the differential equation representing the family of straight lines y = Cx + 5, where C is an arbitrary constant.

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}, \\ y=Cx+5.....\left(1\right) \\ \Rightarrow \frac{dy}{dx}=\mathrm{C} \\ \mathrm{Substituting}\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{C}\mathrm{in}\left(1\right),\mathrm{we}\mathrm{get} \\ y=\frac{dy}{dx}\times x+5 \\ \Rightarrow x\frac{dy}{dx}-y+5=0 \\ \mathrm{Hence},x\frac{dy}{dx}-y+5=0\mathrm{is}\mathrm{the}\mathrm{differential}\mathrm{equation}\mathrm{representing}\mathrm{the}\mathrm{family}\mathrm{of}\mathrm{straight}\mathrm{lines}y=\mathrm{C}x+5,\mathrm{where}\mathrm{C}\mathrm{is}\mathrm{an}\mathrm{arbitary}\mathrm{constant}. \end{gathered}$$