I read Rota's essay today, having already taught the "cookbook" ODE course 5 or 6 times. While the essay carries a lot of wisdom, I think the answer of Nov 25 '18 at 23:18 by guest is absolutely the most useful.

With non math majors, you must strike a balance between concrete and conceptual and most of the suggested books are way too advanced for this level (you will lose most of the students).

Finally, while I guess I subscribe to Rotas arguments, another perspective might be that teaching (some) tricks is not necessarily a bad thing especially if you can deconstruct the tricks for the students. There is nothing dirty about such an exercise well done.