The Solution of differential equation $xdy - ydx = 0$ represents

Given that, $xdy - ydx = 0$

$\Rightarrow$ $xdy = ydx$
$\Rightarrow$ $\frac{{dy}}{y} = \frac{{dx}}{x}$

On integrating both sides,

we get
$\log y = \log x + \log C$

$\Rightarrow$ $\log y = \log Cx$

$\Rightarrow$ $y = Cx$

which is a straight line passing through origin.