@nm 
Thank you. I added as a PS the worksheet containing the tracelast output, which is what allowed for reproducing the problem and fix it. And thanks to @aroche for his quick fix. The fix is already uploaded in the latest Maplesoft Physics Updates for Maple 2024, so to activate the fix, as usual, open Maple and input Physics:-Version(latest).

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

@nm 

Generally speaking, the more extensive is your post, the most unreadable and time-consuming. I suggest you to try to make your reports more compact. By the way, I work with GUI. Always try GUI first. If I cannot reproduce I move into 1D Math input, then TTY.

Now on the issue: there is a bug in the subroutines of `simplify/common/factors`. I passed the problem to the person who wrote the routine, I suppose we will have a fix probably by the end of tomorrow or Friday. Regarding your comments about whether you display or not things ... I don't know. The bug - restricted to the input to the mentioned routine, however, is reproducible no matter what you display.

Best

Thanks Austin, for the so quick fix; it is uploaded now within the Maplesoft Physics Updates v.1793. To install: open Maple and enter Physics:-Version(latest)

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

@C_R 
It is too time-consuming to answer about the details, but here are more comments. I think your approach, "based on observations", is the right approach, always. The page ?dsolve,setup is relevant only for those who want to have a glimpse on how dsolve is coded, its logic, and perhaps change the way it works. It is not a page of interest for many people. Its existence, perhaps, is more related to my academic origin/teaching: do not present black boxes, and never fall for "I know better". For the same rasons you have the PDEtools:-Library and its help page. Regarding the formulation known as d'Alembert's method, this method is present there, under `dsolve/methods`[1, high_degree]. The page on dsolve's setup could perhaps say "everything starting with 1 in eq.(1) of the page is about methods for 1st order ODEs".

Regarding PDEtools: I wrote this package before moving to Canada, then immersed myself into coding a new ODE solver and the symmetry methods for ODEs, followed by extending PDEtools with symmetry methods for PDEs, finally rewriting the DifferentialAlgebra package. I suppose that due to this historical sequence these two packages PDEtools and ODEtools (this one exists only on background, invisible) are strongly intertwined, and connected with the three differential elimination packages mentioned in PDEtools:-casesplit.

In the end, once you realize that from a solving-logic point of view all these things are differential equations of different orders and number of independent variables, the distinction between ODEs and PDEs (or even non-differential equations) is of little relevance: the majority of the tools for PDEs are of use for ODEs. And some commands are indeed present in both DEtools (the visible package for ODEs, not PDEs) and PDEtools, like casesplit, dpolyform, diff_table, dsubs, ... More important: the subroutines presented in ?PDEtools,Library, are used all around in the ODE code.

Regarding your last question, there is a help page, ?dsolve,education, that presents most things, though indeed not an example as the one discussed in this post (branches and related stuff). It may be good to add such an example. Still, the documentation for differential equations is already so large and detailed that adding more may help in some way but, on the other hand, adds clutter. In part, for that reason, I wrote the odeadvisor and its help pages together with dsolve - trying to provide a more structured way to peek at what dsolve does. Anyway, I will think about one more example.

Finally, I share your impression that "studying ODEs with a textbook" does not make sense. In my case, I learned about symmetry methods to then discover the standard classifications shown in textbooks (mainly Kamke's and Zwillinger's) and note that they were only a minimal subset of particular cases of symmetries or integrating factors.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

@vv 
Yes. It is adjusted in v.1786 of the Physics Updates.

@vv 
You are right. And although the FunctionAdvisor cannot list all possible formulae, these ones, related to Mittag-Leffler's theorem, actually not only for tan, are relevant; Wolinski is also right. I missed all these when coding the FunctionAdvisor. For tan, the issue is resolved installing the Maplesoft Physics Updates v.1875 or newer, just uploaded. As usual, to install, open Maple and input Physics:-Version(latest);

The change includes a change in convert(tan(z), Sum), and this is a pic of the FunctionAdvisor output (btw, originally called FunctionWizard .. I liked that name more :)

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

@dharr 
This Warning appears in the updated Maple 2024.1, as per this image, all in TTY with no initialization and only the libraries of the main installation:

I know from where is this "Warning" coming (the DifferentialThomas elimination package); will take a closer look later today.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

@KM4 , @Josecherukara

Download perturbed_metric_(general_case_reviewed).mw

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft​​​​​​​

@KM4 , @Josecherukara
I will return to this today, or tomorrow, and prepare a worksheet showing how.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

@nm 
The Maplesoft Physics Updates is just a package. Not a web server that performs operations on your computer. This sentence you wrote: "It seems Physics updates the version number first, then next it downloads the actual updates." is incorrect. If the file is not updated, it is about rights in your computer or else something in the interaction of PackageTools and the MapleCloud server.

I also note that the file is updated correctly in my computer. Have you tried it in one of your other computers?

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

@nm 
This is what I get running your worksheet just posted, after checking that there is no initialization whatsoever, nothing interfering (BTW have you tried running this in cmaple?) :

So I get the right, expected result, not an Error interruption. And the date is not July 25, though also not yesterday. That is puzzling. I will take a look at the related internals later today.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

@yvnog 
This is a different question ... Have you tried opening Maple, and in an input line, enter > Physics:-Version(latest), press Enter, and wait for the package to get installed? If that doesn't work, would you mind please to take a screen shot so that we can see the message? Thanks.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

Hi @Josecherukara 
Could you please upload a worksheet (use the Green arrow) with your attempt and where is that you don't know how to move forward?

Best!

I will take a look at this today.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

It means that your ODE, of third order, got reduced in order by one, and the resulting 2nd order linear ODE is not solvable with the current algorithms, but its solution can be represented with DESol, (equivalent to RootOf but for differential equations). So, since the order got reduced by one, you see an integration constant around, that appeared in the reduction process. @C_R 's explanation below is equivalent to this one.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft