The solution of Laplace's equation within a Classical Electrodynamics course is fundamental for the understanding of boundary problems in Electrostatics. In the present research work the analytical and numerical solution is obtained by the relaxation method, of a problem of infinite parallel plates, of the Laplace equation in Cartesian coordinates in an Euclidean space of two dimensions, specifically using the Python programming language, for its use in the teaching of Physics and its better phenomenological understanding. Likewise, the solutions obtained by both solution techniques are compared and discussed.