Write the differential equation obtained by emliminating the abit… - Vidyadip

Question

Write the differential equation obtained by emliminating the abitrary constant C in the equation $\text{x}^{2}-\text{y}^{2}=\text{C}^{2}.$

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Answer

We have,
$\text{x}^{2}-\text{y}^{2}=\text{C}^{2}$
Differentiating with respect to x, we get
$2\text{x}-2\text{y}\frac{\text{dy}}{\text{dx}}=0$
$\Rightarrow 2\text{x}=2\text{y}\frac{\text{dy}}{\text{dx}}$
$\Rightarrow \text{x}\ \text{dx}=\text{y}\ \text{dy}$
$\Rightarrow \text{x}\ \text{dx}-\text{y}\ \text{dy}=0$
Hence, $ \text{x}\ \text{dx}-\text{y}\ \text{dy}=0$ is the differential equation.

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