The solution of differential equation xdy - ydx = 0 represents

Given that, 

$\begin{array}{l}xdy-ydx=0\\ \Rightarrow xdy=ydx\\ \Rightarrow \frac{dy}{y}=\frac{dx}{x}\end{array}$

On integrating both sides, we get

$\begin{array}{l}\log y=\log x+\log C\\ \Rightarrow \log y=\log Cx\\ \Rightarrow y=Cx\end{array}$

which is a straight line passing through the origin.