Question

The general solution of the differential equation \(\frac{ydx-xdy}{y}=0 \) is

• A. xy=C
• B. \(y=Cy^{2}\)
• C. \(y=cx\)
• D. \(y=Cx^{2}\)

Answer 1

The Correct Option is C

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.