This article presents some technical and pedagogical considerations about a series of videos made by the authors to teach elementary theory of differential equations. Intended to be a pedagogical support for undergraduate students of scientific curricula, these videos provide rigorous mathematical contents in a form that takes into account the specificities of the tool. Videos for teaching mathematics should be seen as a specific way for providing rigorous scientific content to learners, and should not be reduced to oral manuals or standard classroom lessons. Research Contribution: Arij Bouzelmate and Benoît Rittaud are searcher and teacher in mathematics. Arij Bouzelmate is a specialist in partial differential equations and director of LaR2A. Benoît Rittaud is a specialist in discrete mathematics and is involved in popularization of mathematics.