Question

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

• A. $xy=C$
  
• B. $x=C{y}^2$
• C. $y=Cx$
• D. $y=C{x}^2$

Answer 1

Answer: (C)

$y=Cx$

$\frac{ydx-xdy}{y}=0$

$\frac{ydx-xdy}{xy}=0$

$\frac{1}{x}dx-\frac{1}{y}dy=0$

Integrating both sides, we get,

$log|x|-log|y|=log|k|$

$\frac{x}{y}=k$

$y=\frac{1}{k}x$

$y=Cx$ where, $C=\frac{1}{k}$

Hence, C is the correct option.