The differential equation of the family of circles passing through the origin and having centres on the x-axis is
1
\(2{\rm{xy}}\frac{{{\rm{dy}}}}{{{\rm{dx}}}} = {{\rm{x}}^2} - {{\rm{y}}^2}\)
2
\(2{\rm{xy}}\frac{{{\rm{dy}}}}{{{\rm{dx}}}} = {{\rm{y}}^2} - {{\rm{x}}^2}\)
3
\(2{\rm{xy}}\frac{{{\rm{dy}}}}{{{\rm{dx}}}} = {{\rm{x}}^2} + {{\rm{y}}^2}\)
4
\(2{\rm{xy}}\frac{{{\rm{dy}}}}{{{\rm{dx}}}} + {{\rm{x}}^2} + {{\rm{y}}^2} = 0\)