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

Answer: (C)

$y=cx$

Answer 2

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.