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# True-or-False: The differential equation representing the family of circles $x^2+(y-a)^2=a^2$ will be of order two.

$\begin{array}{1 1} True \\ False \\ can\;not\;be\;determined \end{array}$

Toolbox:
• If the given equation has $n$ arbitrary constant,then the required differential equation will be of $n^{th}$ order
The differential equation representing the family of circles $x^2+(y-a)^2=a^2$ will be of order two.
The above equation has only one arbitary constans $'a'$
we know that if the equation contains $'n'$ arbitary constants, then the required differential equation will be of the $n^{th}$ order
Since the above equation has only one arbitrary constant, the differential equation representing this equation be of order one
Hence the above statment is $False$