This is standard an unavoidable. There are like a dozen of tricks that solve a few special cases, and they were found after heroic brute force search in the void. (The real fact that is somewhat hidden is that most differential equations can't be solved analytically. You solve analytically only the few cases that are solvable analytically, otherwise you just get a numerical solution or an approximation.)
> In this way there was not a lot to discuss, and from time to time the professor would gently steer us back to merely copying and memorizing the methods, even though no one had questioned him out loud.
This is standard an unavoidable. There are like a dozen of tricks that solve a few special cases, and they were found after heroic brute force search in the void. (The real fact that is somewhat hidden is that most differential equations can't be solved analytically. You solve analytically only the few cases that are solvable analytically, otherwise you just get a numerical solution or an approximation.)
> In this way there was not a lot to discuss, and from time to time the professor would gently steer us back to merely copying and memorizing the methods, even though no one had questioned him out loud.
That's a horrible way to teach.