Tangental anecdote: Every time I see Diff EQ mentioned the first thing that pops into my head is the number 11. That's the score of my first, last, and only Diff EQ test. 11%.
I remember my undergraduate mechanical vibrations class. Every exam was basically a test of how well you could do the Laplace transform on some linear ODEs. I memorized the most common transforms, so this became fairly straightforward and fast for me, but it was obvious the other students were struggling.
If I had a problem that wasn't solveable with the Laplace transform, say a linear ODE with variable coefficients, I'd likely take longer to do the exam, but those never appeared in the class.