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I was surprised that there isn't already a section on the List of Generalizations of Common Questions for differential equation questions. I'm especially thinking of those cookbook type "How do you solve [this kind] of ODE?" questions that come up in an a typical introduction to differential equations class. Those must get asked all the time here as homework questions right? There must be some canonical Close as Duplicate targets for those.

Could someone who is more knowledgeable than me of the ODEs questions on this site start this list?

In particular I was looking for a canonical "How do you solve an exact differential equation?" question, in case anyone knows a good candidate for that ;) The various ways to search the site failed me on this one:

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  • $\begingroup$ Unrelated, but has there been any discussion on the SE Meta site about improving the search algorithm? Like, the site's builtin search sucks. Does the search not take into account question scores at all when sorting just be relevance? $\endgroup$
    – Mike Pierce
    Jul 10 '20 at 15:52
  • $\begingroup$ As for most lists of posts there are buttons on the top and you can decide, relevance, active, votes. $\endgroup$
    – quid Mod
    Jul 10 '20 at 16:43
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    $\begingroup$ @Mike This is orthogonal to your point, but SE search is quite bad. Have you tried Approach0? $\endgroup$
    – Xander Henderson Mod
    Jul 10 '20 at 16:43
  • $\begingroup$ You could add that section, @MikePierce. $\endgroup$
    – amWhy
    Jul 10 '20 at 20:03
  • $\begingroup$ @amWhy I could, BUT I'm not familiar with the differential equations questions on this site. Not at all my field. I figure there's someone who could do this job much more easily. Like, I actively ignore the differential equations tags, so I have no idea what the common questions even are, let alone how to find their canonical duplicate. $\endgroup$
    – Mike Pierce
    Jul 10 '20 at 23:23
  • $\begingroup$ Then you might not even know whether such a canonical question is appropriate, or worth the effort, @Mike? $\endgroup$
    – amWhy
    Jul 10 '20 at 23:26
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    $\begingroup$ @amWhy Sure. But I suspect it is appropriate given the number of "how do you solve this exact DE?" sort of questions: one, two, three, four, five, six, seven, etc $\endgroup$
    – Mike Pierce
    Jul 10 '20 at 23:32
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    $\begingroup$ @Mike There are also tons of other repeated sorts of questions across a hundred domains of math on math.se. Given your own acknowledgement that this is not your forte, let someone who follows the tag lead the way. And not all such questions can be answered with one subsuming canonical answer. $\endgroup$
    – amWhy
    Jul 10 '20 at 23:38
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    $\begingroup$ @amWhy "let someone who follows the tag lead the way" ... that's literally what I'm asking for in this Meta post. $\endgroup$
    – Mike Pierce
    Jul 10 '20 at 23:39
  • $\begingroup$ But you assume such a canonical post is needed, which will cover all questions on exact DE's. What I meant was, a person more familiar with the tag should be posting on meta, suggesting what should be done, if anything, not someone who admittedly doesn't even know the tag well enough to ask that something should be done, @Mike. $\endgroup$
    – amWhy
    Jul 10 '20 at 23:41
  • $\begingroup$ @Mike I wouldn't propose that there be one canonical question covering all questions about abelian, non-cyclic groups. $\endgroup$
    – amWhy
    Jul 10 '20 at 23:43
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    $\begingroup$ All credit to Mike for noticing a possible gap in our List of Generalizations thread. It shouldn't be hard to write up a good and useful answer to "How do you solve an exact differential equation?" It would be harder to write up a useful answer telling users how to recognize an exact equation when they see one, and I suspect that often the difficulty the user has is in not knowing it's a good idea to check whether a DE is exact. Perhaps there has to be a generalized question, "What do I do when faced with a Differential Equation?" and then the answer could go through a check list (continued) $\endgroup$
    – Gerry Myerson
    Jul 11 '20 at 0:54
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    $\begingroup$ (continued) of the different common types of ODE and how to recognize and solve each type. $\endgroup$
    – Gerry Myerson
    Jul 11 '20 at 0:55

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