This was, along with 18.06 Linear Algebra, the first math class I took at MIT. Prof. Collins started early on by asking the most important question of the class: "Which countries are doubly landlocked?" I answered "Liechtenstein and Uzbekistan"; the latter became a recurring theme for our problems.
The class contained intuitive concepts; nevertheless, they demanded significant practice, particularly when multiple techniques were presented for solving different systems of differential equations. The main challenge of 18.03 was finding a thread to weave together the whole semester (something other than Uzbekistan, which showed up every so often in lecture check-ins/warm-up problems).
Plotting diagrams became an important part of the class when phase plane diagrams were introduced, and mathematical software (e.g. WolframAlpha) was vital for experimentation and characterization of differential equations.