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I suspect that the inquiry was probing the radiation reaction force.
If you include the "self force" of radiation reaction:
F_s = (q^2/6*PI*epsilon*c^3)*(da/dt), where the derivative is the "jerk",
then a lone electron follows the DE:
mx'' =(q^2/6*PI*epsilon*c^3) *x''' , where ' denotes a time derivative.
This has solutions in which the electron flies off to infinity almost
instantaneously.
This is an unsolved problem and points to the limitations and difficulties
inherent in the model of the electron and the consequent calculation of
Fs.