Write the order of the differential equation of the family of circles of radius r.

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.