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Question
Write the differential equation obtained by eliminating the arbitrary constant C in the equation x2 − y2 = C2.
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Solution
We have,
\[ x^2 - y^2 = C^2 \]
Differentiating with respect to x, we get
\[2x - 2y\frac{dy}{dx} = 0\]
\[ \Rightarrow 2x = 2y\frac{dy}{dx}\]
\[ \Rightarrow x dx = y dy\]
\[ \Rightarrow x dx - y dy = 0\]
Hence, x dx - y dy = 0 is the required differential equation .
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