Ten lessons I wish I had learned before teaching differential equations (1997) [pdf]
Where can I find an expansion of the intuitive explanation given for integrating factors?<p>&gt; It is of the utmost importance to explain the relation between the solutions of the differential equation and the solutions of the system. The solutions of the system are trajectories, they are parametric curves endowed with a velocity given by the vector field. The solutions of the corresponding differential equation are integral curves, and their graphs are the graphs of the trajectories deprived of velocity. Often, instead of solving the differential equation, it is more convenient to solve the corresponding autonomous system.