Answer :

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.


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