Gujarat BoardEnglish MediumSTD 12 ScienceMathsDIFFERENTIAL EQUATIONS1 Mark
Question
Write the differential equation obtained emliminating the arbitrary constant C in the equation xy = C2.
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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.
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