Differential equations

In applications, the differential equations that are most naturally introduced are autonomous differential equations, which are studied in the context of dynamic systems ( ) and linear differential equations ( ), possibly non-autonomous, which model simple maintained systems. The most general differential equations, those which are the subject of this article, nevertheless offer the least artificial framework for studying complex phenomena governed by a continuous law. Their study also makes it possible, under stronger assumptions, to obtain the theoretical results required for the analysis of autonomous equations. In addition, the qualitative techniques dedicated to them apply, mutatis mutandis, to autonomous and linear differential equations. The use of computers can be of great help, both in the exact and approximate resolution of these equations and in their qualitative study. The exact (formal) calculation of solutions to certain classes of differential equations will be the subject of a separate article.