Question:
The solution of \(\dfrac{dx}{x}+\dfrac{dy}{y}=0\) is
The solution of \(\dfrac{dx}{x}+\dfrac{dy}{y}=0\) is
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\(\ln A+\ln B=\ln(AB)\). Replace \(e^{C}\) by a new constant \(k\).
Updated On: Oct 17, 2025
- \(x=ky\)
- \(\dfrac{1}{x}+\dfrac{1}{y}=k\)
- \(x+y=k\)
- \(xy=k\)
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The Correct Option is D
Solution and Explanation
Idea. Integrate each fraction; logarithms add. Exponentiate to remove \(\ln\).
\[ \ln|x|+\ln|y|=C\Rightarrow \ln|xy|=C\Rightarrow xy=e^{C}=k. \]
\[ \ln|x|+\ln|y|=C\Rightarrow \ln|xy|=C\Rightarrow xy=e^{C}=k. \]
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