We discuss two problems which grew out of an introductory differential equations class but were solved only later, each after having been put into a different context. First, how do you find a rather complicated Lyapunov function with your bare hands, without using a fully developed theory (while reconstructing the steps leading up to such a theory)? Second, how can you obtain a global picture of the phase-portrait of a dynamical system (thereby invoking ideas from projective geometry)? Since classroom experiences played an important part in the making of this paper, didactical aspects will also be discussed.

No abstract

No abstract

In the published version of this article, on page 9, line 5 underneath formula 20, a typesetting mistake occurred. The corrected formula reads as follows: λ1 0.492, λ2 2.304 and λ3 28.204 Funding Open Access funding enabled and organized by Projekt DEAL.

No abstract