Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSDIFFERENTIAL EQUATIONS1 Mark
Question
Write the differential equation obtained emliminating the arbitrary constant $C$ in the equation $xy = C^2.$
✓
Answer
We have,
$\text{xy}=\text{C}^{2}$
Differentiating with respect to $x,$ we get
$\text{x}\frac{\text{dy}}{\text{dx}}+\text{y}=0$
$\Rightarrow \text{x}\frac{\text{dy}}{\text{dx}}=-\text{y}$
$\Rightarrow \text{x}\ \text{dy}=-\text{y}\ \text{dx}$
$\Rightarrow \text{x}\ \text{dy}-\text{y}\ \text{dx}=0$
Hence, $ \text{x}\ \text{dy}-\text{y}\ \text{dx}=0$ is the differential equation.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.