Exact solution of the Herrera equation of motion in classical electrodynamics

The Landau-Lifshitz equation is derived as a first-order iteration of the Lorentz-Dirac equation for the charged particle. In those cases with null electromagnetic field's gradient, the Landau-Lifshitz gives the so named Herrera equation. A general method for the solution of the latter equation is presented and applied to the motion of a particle in a uniform electromagnetic field.