Question

Write the differential equation obtained by eliminating the arbitrary constant C in the equation x² − y² = C².

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}, \\ {x}^2-y^2=C^2 \\ \mathrm{Differentiating}\mathrm{with}\mathrm{respect}\mathrm{to}x,\mathrm{we}\mathrm{get} \\ 2x-2y\frac{dy}{dx}=0 \\ \Rightarrow 2x=2y\frac{dy}{dx} \\ \Rightarrow xdx=ydy \\ \Rightarrow xdx-ydy=0 \\ \mathrm{Hence},xdx-ydy=0\mathrm{is}\mathrm{the}\mathrm{required}\mathrm{differential}\mathrm{equation}. \end{gathered}$$