[Test0129]

Unfortunately it seems this way with a lot of higher level math and it's not really unique to differential equations. The difference is, unlike calculus in general, in diffeq you have actual rote formulas to solve most of the known solvable cases.

I found the classes to be rote. The derivations are truly non-trivial. The book Ordinary Differential Equations by Arnold goes into more detail. Basically if we taught the reasons we'd require everyone to take analysis and differential geometry to truly understand how they work. Given the MAJORITY of students in diffeq are engineers and not math majors 99.9% don't want to know and/or don't care about this detail. You see a similar occurrence in calculus where you're basically told "dont think about it too hard" for your own safety. If you start wondering a little too hard about calculus you end up switching majors to math and taking two semesters of real analysis. It's also EXTREMELY common for engineering professors to teach differential equations rather than math professors. This further waters down the rigor because (obviously) an engineer will not know/care about the rigor. Part of the reason I've pursued a math degree is because there was so much handwaving in engineering/computer science it became just an extremely annoying grab bag of math tricks and I wasn't satisfied.

To me we have too many inter-dependent classes to teach each class with full rigor. As a result you end up with a collection of half-understandings for most of your undergraduate career and only if you take a math major itself (or a minor in math) will you actually unlock the other half. A better path through math might be basic algebra I, II-> geometry -> trig -> abstract algebra I+II -> analytic geometry -> calculus I, II, III -> real analysis I+II -> differential equations I+II, but this would basically make every degree a math degree. What you experienced is the compromise.