Question

Write the differential equation obtained eliminating the arbitrary constant C in the equation xy = C².

Answer 1

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