The upsetting thing about DiffEq is that the way it is taught has nothing to do with the way it is practiced or used, either by mathematicians or engineers. Sep

The upsetting thing about DiffEq is that the way it is taught has nothing to do with the way it is practiced or used, either by mathematicians or engineers. Separable equations, for example, are the highest order of bullshit. Almost no interesting problems are separable. (Like, there are infinitely more inseparable than separable ones.) The track that should really take over should be one where the student develops the intuition about what related rates of change mean, and then abandon the chicanery of these special-case tricks in favor of the numerical solution of DiffEqs and the evaluation of the quality of the solutions.