@Scot Gould 

Your reply is valuable because you have direct feedback from new users (which I do not have). Its important that they like it and I have expressed this earlier. I still think the new UI can be improved without screwing it up. 

After giving up with the 2025 version (because it was not well integrated into Windows window manager) I do an effort to get used to the new UI. It still feels like these modern cars with a big screen and without hardware keys. I simply want to turn on the wiper with one click and not digging through menus and not beeing distracted with functions that I rarely use. And I want to turn it of with one click. That's why I think customization off quick access buttons could be a way to make everyone happy and me not using F5. I do not care how Maplesoft improves the usabilty in terms of less clicks and less mouse meters. If they have something better, why not.

The toolbars and the quick acces buttons were introduced in the former UI for a good reason. I do not think that the reasons have changed. Maybe they have been forgotten.

Coimming back to F5: I still do not understand why worksheet and document mode function differently when is comes to displaying the state of the entry mode. This could be harmonized.

@Scot Gould 

I have just seen your answer. Here are more details for Maplesoft why I described these indicators as "out of focus".

@Maplesoft: The animated "quick access" buttons in the upper right corner require me to move my head to see them sharp because they are small and have low contrast (dark blue on grey back ground with tiny white details). I avoid these head movements. They make me sick (probably caused by the magnification of my computer glasses which distorts perspective). This is a result of presbyopia which about one third of the population has to deal with. I use other ribbon applications that emphasize details with color to make them easier perceivable. 

@dharr 

Where do you see "and I see the change to "non-executable"" this?

Do you mean in the status bar?

This does not indicate the exact mode and I end up with executable math in text passage (conceptually I always thought that document blocks were introduced for this).

Edit:

I overlooked where you saw the change of mode. The extra click to edit tab is one of the too many clicks (as compared to the Maple 2024 UI). So I do not do this whenever I can avoid it. An option to save this extract click could be to swtich automatically to the edit tab after inserting a text paragraph with

(Inserting a text paragraph also often requires an extra click which was not required in the former UI.)

Thank you for verifying.

@Ronan 

I checked with Maple 2024. In worksheet mode, a text table is inserted as you described it. In document mode a table with 2-D Math input is inserted.

@dharr

I would also have expect that this call

returns the output unevaluated and adds an index

The evaluation rules of procedure call and how a statement (example in @acer answer) is treated seem to be different.

I hope I will remember this. Those cases are reare.

Thank you all

@dharr 

This would make more sense. For me, in equation (1) there is too much room for misinterpretation.

What I am looking at? Is it pure nonsense because of impropper initial conditions posed here.

@acer 

Concering _a I missed exact terms. I read somewhere "parameter".

Yes I want _a in the outer RootOf (yellow) not beeing used in the inner RootOf (green) in case they are not the same. The _a encircled in red is something I have difficulties to interprete. Why is this ??? named the same as the variable of integration?

What Root is returned? The value of _a

@acer 

Yes! That's what I was looking for. Did you use the large model? Maybe asking more than once increases the success rate. This would mean that prompts are not separate. I interprete this as yes

Thank you

@acer 
Thank you. I realised in the meantime that a change in sign only shifts the phase portrait by pi with the implication that
for x->infinity the limiting value for the angle will become _Z*2*pi (_Z depending on the ICs). 

@sand 
You mention conservation of energy. The consequence is that only one initial condition is needed. The other IC can be deduced from it. The need of only one IC to find a solution for a second oder ODE is something I was never happy with. Now I have a satisfying explanation.
I assume that the difference in the solutions can be resolved by adding here an integration constant that takes an appropriate initial velocity into account.

ode_2 := map(int, ode_1, x);

This should remove _C1 from your solution.

By the way: Including laws of physics is not required. I googled a bit. Treating the system as a hamiltonian system and seeking a scalar function $H(y,y\_dot)$ that is constant along the trajectories of the flow in phase space leads to the same result as conservation of energy.
What makes this "finding" (for me) interesting is its implication on partial solutions of ODEs and testing them.
The existance of such scalar functions restricts possible solutions and in the context of 

@nm question of testing odes could provide conclusive answers. I have to think about it.

Maybe the archtitect of odetest @ecterrab can tell if it would make sense to make odetest even more powerfull in this sense. Maybe it is already.

@sand15 
I am getting an error here with Maple 2025

I did expect to see multiples of pi, not fractions. 

In eq(1) there is a sign missing. I am not sure if than makes a difference on the results

@TechnicalSupport 

After your response I could sort out the misunderstanding with support and transferred the Maple.ini files. 

As you might have seen, my original mail was in my mother tongue to a support address that I have used for years. I did expect a reply from staff that I have known for years. The reply from a new person was most likely machine translated (as my original mail was probably also machine translated). The process of back-and-forth translation is not perfect and might have contributed to my impression that I was talking to a bot. What adds to this impression is the almost too perfect and polite wording of the replies. On my side, I am AI fatigued, which has also contributed to the wrong suspicion.

Anyway, thank you for clarifying. This is important. 

@acer 

Thanks for clarifying! 

@Paul 

If I understand correctly Mathpix (and not OpenAI) is performing the document import.

Thank you for the clarification

@aroche 

Done already. Thank you for following up!