Answer :


Differential Equation of the family of circles touching X-axis at the origin is


= x2 + (y – k)2 = k2


Here (0,k) is the center of the circle and radius k.


= x2 + y2 + k2 – 2 × k × y = k2


= x2 + y2 – 2 × k × y = 0 ---(1)


Differentiate w.r.t x we get,





Put value of k in (1) we get,




is the differential equation of the family of circles touching X-axis at the origin.


Here the order of differential equation of the family of circles touching X-axis at the origin is 1.


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