Question:
The general solution of the differential equation \(\frac{ydx-xdy}{y}=0 \) is
The general solution of the differential equation \(\frac{ydx-xdy}{y}=0 \) is
Updated On: Sep 13, 2023
xy=C
\(y=Cy^{2}\)
\(y=cx\)
\(y=Cx^{2}\)
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The Correct Option is C
Solution and Explanation
The given differential equation is:
\(\frac{ydx-xdy}{y}=0\)
\(⇒\frac{ydx-xdy}{xy}=0\)
\(⇒\frac{1}{x}dx-\frac{1}{y}dy=0\)
Integrating both sides,we get:
\(log|x|-log|y|=logk\)
\(⇒log|\frac{x}{y}|=logk\)
\(⇒\frac{x}{y}=k\)
\(⇒y=\frac{1}{k}x\)
\(⇒y=Cx \:where \:C=\frac{1}{k}\)
Hence,the correct answer is C.
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