The differential equation of all circles passing through the origin and having their centres on the $$x$$-axis is

A

$$x^2 = y^2 + xy \frac{dy}{dx}$$

B

$$x^2 = y^2 + 3xy \frac{dy}{dx}$$

C

$$y^2 = x^2 + 2xy \frac{dy}{dx}$$

D

$$y^2 = x^2 - 2xy \frac{dy}{dx}$$