  It is well known that the third-order Lorentz-Dirac equation admits runaway
solutions wherein the energy of the particle grows without limit, even when
there is no external force. These solutions can be denied simply on physical
grounds, and on the basis of careful analysis of the correspondence between
classical and quantum theory. Nonetheless, one would prefer an equation that
did not admit unphysical behavior at the outset. Such an equation - an
integro-differential version of the Lorentz-Dirac equation - is currently
available either in 1 dimension only, or in 3 dimensions only in the
non-relativistic limit.
  It is shown herein how the Lorentz-Dirac equation may be integrated without
approximation, and is thereby converted to a second-order integro-differential
equation in 3D satisfying the above requirement. I.E., as a result, no
additional constraints on the solutions are required because runaway solutions
are intrinsically absent. The derivation is placed within the historical
context established by standard works on classical electrodynamics by Rohrlich,
and by Jackson.
