Around 50 years ago, I was a math major and consequently required to take a course on differential equations. For perhaps the first time, I was taking a class on mathematics that just didn't click for me; nothing was intuitive. The class was just a big bag of complicated tricks. Each category of differential equations covered in the course had its own special trick. There was no general or universal approach to solving a DE; one had to recognize a particular problem was a DE from a particular category and apply the special trick to solve it. The methods were often long or complex and they only solved some differential equations. Many differential equations have no trick at all to solve them. It turned out to be a tough class for me because I'd never before needed to learn math purely by rote.

Those that have taken Integral Calculus may be thinking that solving DEs sounds akin to integration where one may have to apply substitutions, integration by parts, trigonometric substitutions, or partial fractions. Yes Calculus requires learning a bag of trick too, buts its a small bag of simple tricks with wide applicability. So many of the functions one needs to integrate succumb to this small bag of tricks that it's almost fun to hone ones technique. A class on elementary differential equations is just depressing.

To be fair, differential equations are important. Physical phenomena are often best described by differential equations. Fortunately, programs like Mathematica can be used to tackle real world differential equations one way or another (perhaps with numerical methods) to obtain solutions.

I was fortunate to have my Probability course (sadly, not my differential equations course) taught by Gian-Carlo Rota.