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