@janhardo I guess my toy example has no closed-form solution. For me as a physicist and physics educator, that is rarely an important issue.  

Note: Thanks for introducing me to Student:-ODEs:-ODESteps.  It is pretty cool. I will show it to my students. They will groan because they have spent weeks practicing how to solve ODEs without the use of a computer. 

@janhardo  My apologies, but I don't understand your question. Are you referring to how I wrote the equations, or are you referring to how the solutions are presented in blue?  I wrote the expression for the derivatives as y’ or y’’, but I could have written them as y’(x), y’’(x).

This is a good problem that comes up so frequently for me that I would like to see the smart folks here provide some constructive feedback.  

My goal : solve using the most readable and simplest solution for the non-expert / occasional user of Maple. 

Here is my approach: solve the ODE with initial conditions numerically with the output as a list of procedures:
 

Note: I tried to post my worksheet,  but MaplePrimes, which displayed it, failed to post it. 

Root_of_numeric_ODE.mw

@rcorless  I love "add" and I agree about the difficulty in reading Kitonum's solution, but I read the request by the OP differently.  I read it as he wanted each term written out separately.  The "add" solution provides a single term.  

(I attended a workshop run by a long-time Maplesoft coder/ engineer. He too said that any expression which included the back-tick marks, is less than elegant. That is why he codes with ifelse instead of `if`. ) 

@mehdibaghaee 

Download Atomic_Variable_vs_Indexed_Variable.mw

@acer I like your solution. I've also used plots:-display(Vector[row](plot1, plot2, plot3)) for plots inline.  And yet, in both cases, is it possible to force the plot to appear in the center of the square? In my solution, they all align with the left. 

@janhardo  Are you aware that on an execution group the key F5 switches between 2d input and "text" which is 1d Maple input?

@acer This may be first time I believe I saw an error in your answer. 

In the loop 

  for i to 5 do

the loops starts with a default of 1, not 0. 

Even the most common method:  a := 'a'    does not work. (And left quotes characters generate an error.) 

Maple Flow is new and the programmers need such feedback. 

@charlie_fcl I don't appear to have that file on my Windows version. Sorry, I can't help out, but I would be interested in what you see. Can you post a screen shot here? (Heck, you could even email me a copy of the file.)

@charlie_fcl I understand ... and can reproduce this odd error. I guess the simple answer for now is, "If it hurts when you move your arm that way, then don't move your arm that way."

I suspect your post here will generate a bug report. (I wasn't able to generate one on the beta site.) 

Can you provide a link, or more details as to where you saw this file mapleflowrc, please? 

As for my copy of MapleFlow 2021.2, there are only 4 palettes: Expression, Units, Greek and Matrix. Personally, I would like to see more palletes. Help shows no way to include more palettes as one can do in Maple. 

I too copy into Word documents on ocassion. 

I notice that when posting from 2021.2 to Word 365 (Windows), the 2D plot "pastes" correctly, but the 3D plot does not, regardless how the copy command is performed. Fortunately, "Snip and Sketch" does work properly for both plots. 

I suspect someone at Maplesoft will test such transactions and get back to us. 

Maplesoft is aware of this problem.

The best I've seen for programmatically setting the fps value was answered here: https://www.mapleprimes.com/questions/232716-How-To-Change-Programmatically-The-Number which I agree is less than intuitive. 

Otherwise, given the default of 10 frames-per-second, yes, for a long process then lots of frames are generated. (frames = time * fps) However, at worst, the maximum error for the entire period of the animation should be within 1/20th of a second.  Increasing the fps would decrease the error.

I would like to see Maplesoft add 'fps' = as an option in plots:-animiate, if possible. Based on a search here in Maple Primes, this request is at least 10 years old.