We investigate the Hyers–Ulam stability (HUS) of certain second-order linear
constant coefficient dynamic equations on time scales, building on recent results for first-
order constant coefficient time-scale equations. In particular, for the case where the roots
of the characteristic equation are non-zero real numbers that are positively regressive on
the time scale, we establish that the best HUS constant in this case is the reciprocal of the
absolute product of these two roots. Conditions for instability are also given.
