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