This is so important. My precalc instructor was boring AF and I remember none of it. My DiffEQ instructor got so carried away that the prof next door would come over and tell him to stop banging on the chalkboard. As a result, I think DiffEQ is the fundamental magic that makes the world go 'round.1. Be as excited as you can be. Rigorous argument is not necessarily the most enthralling of things, but people pick up on whether you care about something and that can make a big difference in their opinion of the topic.
It's funny because mine was math so pure that the final was "Imagine a function that does xxxxxxxxxxx. What would happen if A) yyyy? B) zzzz? C) ppp ddd qqq?" No numbers. Fuckin' essay-style with roll-your-own functions and derivation. It was eye-poppingly hardcore. The rate of attrition in that class was such that 15% of the people who started it finished it. I got a 25% on the one assignment he gave all quarter and immediately asked him what I could do to resurrect my grade. he said "relax! You were in the top 20%!" When all of us were heads down and desperate on that final he said "if you take it home and study I will give you an A." Fuckin' A I'll bet I could teach Diff EQ even now and it's been 20 years. That class was goddamn amazing.
Maybe it was my professor - he was basically like "here's a Laplace and this is how you calculate a Wronskian so go do that now okthxbai". He never explained why things were done that way properly, so I had to resort to fucking Khan Academy more than once to understand what was happening.