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
Again differentiating above equation w.r.t x
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.
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