Why do differential equations inspire such fear and loathing in math students?

Usually it's a lack of understanding exactly what needs to be done to the equation and in what order. If the student isn't confident in the fundamentals of algebra they'll also find it difficult because now they not only aren't entirely sure what to do with the calculus part, they're not sure what to do after they've applied calculus with the equation that's left over.

A lot of lower level mathematics is taught algorithmically (i.e., "plug & chug" math). So long as you recognize what the problem is (i.e., do you need to differentiate or integrate or do something else first?) then you can usually solve it just by applying what you were shown in class and what the problems you were assigned reinforced. Of course teachers like to show you easy problems in class and then assign problems or give problems on tests that, on the surface, look nothing like what they used as examples. In reality these problems really are quite similar, they just look more intimidating. This is one of the problems with "plug & chug" math is that they show you how to do manipulations by rote, "If you see this, do this" sort of thing and then they give you homework or test problems that they expect you to actually think about and recognize as being the same thing as the examples, but they don't necessarily tell you how to recognize that fact. This is often where algebra fundamentals comes in or simply being very familiar with the topic the homework/test is covering. Without those two things the teacher can present a problem that was one from the classroom example that has been manipulated one additional step and a lot of students will have no idea what to do with it even though they saw the exact same problem (only simplified by one step) in class.

Assuming that you know all of the fundamentals and you're not struggling with the calculus itself then the issue is that some of the problems can just be outright tedious. Once you've applied the calculus (correctly, hopefully) and done the algebra you may be left with a lot of mind-numbing arithmetic. Do that for a few hours and you'll hate the class, even if you completely understand the material.

/r/NoStupidQuestions Thread