Form the differential equation of all circles which pass through origin and whose centers lie on y-axis as shown below:

Question

$\begin{array}{1 1} (A)\; (x^2-y^2)\large\frac{dy}{dx}-2xy=0 \\ (B)\; (x^2+y^2)\large\frac{dy}{dx}-2xy=0 \\ (C)\; (x^2-y^2)\large\frac{dy}{dx}+2xy=0 \\ (D)\; (x^2+y^2)\large\frac{dy}{dx}+2xy=0\end{array} $