@acer It is all good. The more I read, the better I am informed and the better I can help others. As I said, I have always used the add procedure for these types of situations. But there is no doubt the sum procedure is getting smarter and more innovative. Hence the motivation to learn more. 

@lemelinm I'm probably the number one whiner on the beta test site about how export/print fails to generate a reasonable PDF. But I need to use it all the time, such as on my webpage. In my opinion, the PDF print or export routine has gone backward ever since the implementation of the print layout mode. I like the idea of print layout mode.  But for some reason, the spacing of lines or graphs never works. What you see is not what you get. (2023 was not bad. I simply don't print in 2024 .) 

The folks at Maplesoft are very nice and encourage me to report bugs. However, it wouldn't surprise me if they decide to block my account once the beta of the 2025 version comes out. (For our Canadian friends, that last sentence was an example of sarcasm. 😁 ) 

@acer It was very nice of you to take the time to write out a detailed explanation. However, I would have been offended if you had simply said, "Click on the magenta error message link and READ IT!" The page not only contains an explanation, but it includes the method @nm pointed out. 

Too frequently, the magenta error line leads to no page. Consequently, I never click on it. Lesson learned. Don't assume there is nothing at the end of the magenta link. 

Yes, the help page for the sum summarized what I have told others - use add when adding discrete quantities.  

However, I realize now that I wrote the question poorly. I was more interested in discovering more about what happens internally in Maple. Printlevel wasn't sufficient. Let me do more reading the chapter on Debugging before I return and ask another question that causes me to end up with egg on my face. LOL!

@lemelinm My apologies, Mario. I did find a post you made to one of my videos, the Statistical Mechanics video. Normally, questions that I have not responded to are held for me to work on. This one slipped by. 

 All of my documents, either in PDF or Maple-worksheet format, are found on my web domain, gould.prof. So for the physics ones I'm working on, go to gould.prof/learning-physics . 

@Aung, What is the difference between your original problem and this one? I don't see it. If you identify the only difference, then you might be able to use the same procedure I used.

@acer A fun and informative solution. I saved it so that I can pass it on to others. 

@sidyly1211 Are you satisfied with @acer's solution? 

@Paras31 I don't know why the arrows don't show up. Your system is nearly identical to example 3 in DEtools, DEplot and that one lacks arrows. 

Change your system to y'(t) = u(t), u'(t) = -y(t) and the arrows will appear. Same graph. (And for fun, animate the curve.)

MaplePrimes_DEplot.mw

@acer I enjoyed and valued everything you wrote because it forced me to think again about why I tend to recommend "output = listprocedure" over the default. I recognize the value of odeplot and why it was created. I recognize the speed advantage. However, I value simplicity and maximizing productivity with the fewest amount of commands. Remember to add "pitick" (which I misread as "pit-ick") when it is not necessary violates my philosophy. 

The great thing about Maple is that both new and infrequent users can use it while providing a way for faster calculations for more intensive users.  I evaluate other systems but keep returning to Maple because while others can be simpler to use, there is often a calculation/programming ceiling with them. On the other hand, those without ceilings, such as Mathematica or Python, require more engagement to use at the most basic level. (They have become easier because of github and LLMs.) 

@Paras31 Do you mean that the output of DEplot is not circular? That is because of Maple plots a square box and fits the axes within that square. Include the scaling = constrained option to theDEplot call. The output will be circular.

One other comment. If you are planning to use odeplot, then there is no need to include the output = listprocedure to the call to dsolve. I prefer including the output=listprocedure and then extracting the procedure so that I can treat the procedures as a function. That way, I don't have to remember how to access the elements within the solution module. But not everyone works that way. 

@Christopher2222 As someone who also uploads videos to YouTube, I appreciate you bringing up this question. I pay for my account through my Google YouTube Music subscription. Consequently, I am unaware of what is free and what is not. 

My guess is that Maplesoft is also unaware that one can no longer download the videos for offline viewing. I bet, like my videos, theirs are stored on a computer within their system. An email to Maplesoft might be sufficient to get them to list the links to the videos on their website.  

Have you considered a physical solution instead of looking for a programable solution? There are blue-light-reducing filters for computer screens. There are also blue-light-reducing spectacles. 

@Alfred_

Windows and Unix; ctrl-delete

Mac; command-delete

The two keys are struck simultaneously.

Also. Look for "shortcut keys" in either Help or the Maple Portal under help for other keystrokes of interest.

For the basics, I recommend the thin book "How to get started in Maple" by Doug Meade. I have my own video series based on the book, which is at YouTube/@MapleProf called Learning Maple. You might like Fundamentals 8.