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We discuss the great importance of using mathematical software in solvingproblems in today's society. In particular, we show how to use Mathematicasoftware to solve ordinary differential equations exactly and numerically. Wealso show how to represent these solutions graphically. We treat the particularcase of a charged particle subject to an oscillating electric field in the xyplane and a constant magnetic field. We show how to construct the equations ofmotion, defined by the vectors position, velocity, electric and magneticfields. We show how to solve these equations of Lorentz force, and graphicallyrepresent the possible trajectories. We end by showing how to build a videosimulation for an oscillating electric field trajectory particle case.

Using Mathematica software to solve ordinary differential equations and applying it to the graphical representation of trajectories