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

Question

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