Write the differential equation obtained emliminating the arbitra… - Vidyadip

Question

Write the differential equation obtained emliminating the arbitrary constant $C$ in the equation $xy = C^2$.

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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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