TL;DR: Is there a tag which is intended (only) for ordinary differential equations? If not, should there be one?
The situation with the tags related to ODEs seems a bit unclear to me. AFAICT there is no tag specifically for ordinary differential equations, although they appear as a part of some tags that encompass larger areas. (At least if we follow the guidelines for usage displayed in the tag-excerpts.) I'll try to describe the existing tags - I have also copied the tag-excerpts below.
At the moment there are these tags:
- The top-level tag ca.classical-analysis-and-odes, which covers ODEs but also several other large areas.
- The tag differential-equations, which is (according to the tag-excerpt) both for ODEs and PDEs. (And also for some other types of equations.) This also overlaps with the ap.analysis-of-pdes tag.
- There is also the tag analysis-and-odes, but it is hardly used (it contains only five questions). It has empty tag-info and from the title it is not clear whether this tag was intended to be exclusively about ODEs.
Just for comparison I'll mention that on Mathematics there is a tag called (differential-equations). The tag-excerpt explicitly says that it is for ODEs and not PDEs. (This is not exactly area I am active in, but my estimate is that enough experienced users on Mathematics site know about the distinction between this tag and the (pde) tag and incorrectly tagged questions are usually quickly retagged.)
What should be done about the tags for ODEs here on MathOverflow?
- Doing nothing is also an option. We have two big tags - (ca.classical-analysis-and-odes) and (differential-equations) - which contain ODEs as one of the topics, maybe a separate tag is not needed. (After all, if the asker includes a top-level tag as recommended, it should be possible to find questions about ODEs using the combination of the tags differential-equations+ca.classical-analysis-and-odes.)
- If a separate tag could be useful, one option would be to create a new ordinary-differential-equations tag. (The limit of length of tag names is now 35 characters, it used to be only 25. Perhaps ode and/or odes sound like reasonable candidates for synonyms. And if the tag-name seems too long, the shorter version can be chosen as the master tag.)
- Or the tag differential-equations could be used for this purpose. (I.e., PDEs would be excluded from the tag.) This would mean changing the tag-info and also retagging some older questions. However, I still think that it is better when already the tag name clearly shows what the tag is intended for and askers are able to use the tag correctly even if they do not read the tag-excerpt.
And since I have already made a post about ODE-related tags, it can probably be decided at the same time whether the tag analysis-and-odes can be removed or whether it makes sense to keep it around. (In the latter case, the intended use of this tag should be clarified.)
Here is what the tag-info for the tags mentioned above says at the moment.
The current revision of the tag-excerpt for ca.classical-analysis-and-odes:
Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.
Several of the areas listed there have a separate tag: special-functions, orthogonal-polynomials, harmonic-analysis, calculus-of-variations.
The current revision of the tag-excerpt for differential-equations:
Ordinary or partial differential equations. Delay differential equations, neutral equations, integro-differential equations. Well-posedness, asymptotic behavior, and related questions.
As already mentioned, the tag-info for analysis-and-odes is currently empty. Although the topic here is ODEs, I will include also the current revision of the tag-excerpt for ap.analysis-of-pdes:
Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.