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%.
had you studied at all? most undergrad differential equations classes are fairly mechanical in nature, you just learn to identify the type of problem, then you follow the steps exactly as they are written in the textbook, super little variation or freedom
This is often more true than many believe. But in my experience few students get so far that they recognize the patterns and can respond in the way you describe. That might be the crux.
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.
