# General solution of following differential $\in a ^n$ differential equations of a family of circles passing through the origin and having centre on the x axis
$(a)\;x^2-y^2+2xy \frac{dy}{dx}=0 \\ (b)\;x^2-y^2+2xy \frac{dx}{dy}=0 \\ (c)\;x^2+y^2+2xy \frac{dy}{dx}=0 \\ (d)\;x^2+y^2-2xy \frac{dy}{dx} =0$