  We discuss the great importance of using mathematical software in solving
problems in today's society. In particular, we show how to use Mathematica
software to solve ordinary differential equations exactly and numerically. We
also show how to represent these solutions graphically. We treat the particular
case of a charged particle subject to an oscillating electric field in the xy
plane and a constant magnetic field. We show how to construct the equations of
motion, defined by the vectors position, velocity, electric and magnetic
fields. We show how to solve these equations of Lorentz force, and graphically
represent the possible trajectories. We end by showing how to build a video
simulation for an oscillating electric field trajectory particle case.
