The differential equation of the system of circles touching the y-axis at the origin is

1
\({x^2} + {y^2} - 2xy\frac{{dy}}{{dx}} = 0\)
2
\({x^2} + {y^2} + 2xy\frac{{dy}}{{dx}} = 0\)
3
\({x^2} - {y^2} + 2xy\frac{{dy}}{dx} = 0\)
4
\({x^2} - {y^2} - 2xy\frac{{dy}}{{dx}} = 0\)

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