ABSTRACT
Our goal, in introducing ordinary differential equations, is to provide a brief account on methods of explicit integration, for the most common types of ordinary differential equations. However, it is not taken for granted the main theoretical problem, concerning existence and uniqueness of the solution of the Initial Value Problem, modelled by (4.3). Indeed, the proof of the Picard–Lindelohf Theorem 4.17 is presented in detail: to do this, we will use some notions from the theory of uniform convergence of sequences of functions, already discussed in Theorem 2.15. An abstract approach followed, for instance, in Chapter 2 of [60], is avoided here.
