Let us solve the differential equation

⇒ xdy – ydx = 0

⇒ xdy = ydx

⇒ log y = log x + c

⇒ log y – log x = c

Using log a – log b = log

⇒ y = e^cx

e^c is a constant because e is a constant and c is the integration constant let it be denoted as k hence e^c = k

⇒ y = kx

The equation y = kx is equation of a straight line and (0, 0) satisfies the equation hence