To find the Order we first need to find the differential equation of the family of circles of radius r.

In general, the equation of circle with center (a,b) and radius r is given by,

(x – a)² + (y – b)² = r² ---(1)

Differentiating above equation w.r.t x

---(2)

Again differentiating above equation w.r.t x

---(3)

Putting value of (2) and (3) in (1) we get,

is the required differential equation.

Here the order of differential equation of the family of circles of radius r is 2.