@Preben Alsholm 
 

Thanks, I first created the procedure myself for the spiral field plot.
Then I asked AI (chatGPT) to create the procedure and that is now the code you are working on ..it should be a spiral via DEplot.

It's interesting when you (re)ask the AI to give as many variants as possible of Maple code for the task of showing two differential equations with two initial conditions in a field plot.
The AI never comes up with error-free code,but if you go through the code step by step, you will soon have a start.
In Maple, there are more roads that lead to Rome ( Dutch saying)
 

@Preben Alsholm 
Thanks, the idea is now further, how to make a function of x out of a list [a,b] 
note: keeping a set {a,b}  is probably not working for ~ operator

@janhardo 
If you then look at the AI generated code and step by step the the commands are already wrong .
Maybe in outline right ? 

# Definieer de differentiaalvergelijkingen
eq1 := diff(x(t), t) = y(t);
eq2 := diff(y(t), t) = -x(t);

# Geef de beginwaarden op
beginwaarden := x(0) = 1, y(0) = 0;
                             d             
                     eq1 := --- x(t) = y(t)
                             dt            

                            d              
                    eq2 := --- y(t) = -x(t)
                            dt             

               beginwaarden := x(0) = 1, y(0) = 0

# x := unapply(rhs(dsolve({eq1, eq2, beginwaarden}, {x(t), y(t)})), t);
dsolve({eq1, eq2, beginwaarden}, {x(t), y(t)});
                {x(t) = cos(t), y(t) = -sin(t)}

rhs(dsolve({eq1, eq2, beginwaarden}, {x(t), y(t)}));

? rhs
Error, invalid input: rhs received {x(t) = cos(t), y(t) = -sin(t)}, which is not valid for its 1st argument, expr

To pick the rightside from dsolve :

{x(t) = cos(t), y(t) = -sin(t)}

with rhs in order to make a function of x for cos(t)? : {x(t) = cos(t), y(t) = -sin(t)} 
Can be a sparringpartner the AI for problem solving , if the generated code is useful? 
Well, i stop with this getting the code working
note: i removed the t in the own made procedure: dv_systeemplot and it is working.

@acer 
Thanks, Ah, of course at Questions I must be ....
Want to make the procedure a bit more user-friendly, that would be next.
Will come back to a question on a new topic in due course.

@mmcdara 
Thanks, seems simpler now the procedure without using local variables.
The question comes up, when are local variables defined in a procedure ? 
@acer has already suggested something about this, but what he means exactly is not yet clear to me.

@acer 

Thanks, a simpler approach is also possible it seems.
On the 2nd point, the procedure should also be able to show other 1st-order ODE field plots.
The use of DEplot and dfieldplot to draw a line element field and their use in a procedure.?
Haven't had any intention of how I set up the procedure, so any pros or cons are unknown to me .

"ps. I don't fully understand why you need such a procedure, instead of DEtools:-DEplot (or plots:-odeplot)."

I want to see more line element field plots with integral curves of other 1st order ODEs
A procedure is never natural for one-time use. 
Can also see the line element field via a maplet in Maple itself, but I'm concerned with making of a procedure to understand that better.

Just ask the Maple experts here on the forum what "rootfinding" procedures are available in Maple.
Then we can have a look at finding the intersection points with the x-axis

@C_R 
Thanks, don't know MS Word well, but an easy editor to format a maple document or worksheet seems more convenient than the current system of formatting.

@C_R 

Thanks, just quickly setting a different font and size in the Maple worksheet is not so easy.
You would say a custom worksheet/document editor where you load a worksheet or document and do the character and paragraph adjustments in it would be easier for a user?

@C_R 

Thanks, for the approach to change a worksheet or document font size and font type afterwards.
Also intend to set a new persistent font and size for a new worksheet.
Am not familiar with the use in Mape of styles. 
I suspect you can use the styles to create a new document or worksheet template?

How is Maple supposed to know if the 2 integrals converge?
Ok, i see it are the same integrals , then all chances 

restart;
J := abs(Int(h(x), x = -infinity .. a) - Int(h(x), x = -infinity .. b));
J_final := simplify(eval(J, {a = max(a, b), b = min(a, b)}));
J_final;

Compared to chatGPT public where you can ask anything and the 4 commands in Maple ?
The enormous mathematical knowledge that Maple has that you should be able to manipulate with the language model....
Any mathematical question you need to be able to ask and present in Maple itself.
ChatGPT public free, unfortunately cannot show graphs yet.

restart;
sol := _C3*x^2 - _C1*x + x;
myconstants := indets(sol, And(symbol, suffixed(_C, nonnegint)));
map(X -> :-parse(X[3 .. ()]), map(X -> String(X), myconstants));
n := max(%);
new_constant := _C || (n + 1);

@Carl Love 

Already becomes problematic when I ask the AI package to make a combined plot of the riemann zeta function and an ordinary sine function in Maple
But can the AI still be helpful ? 

Perhaps not surprising that ChatGPT comes up with a comprehensive proof of the primes' indefiniteness, but does compare for me to my earlier proof in old study material.

The current package for AI in Maple gives 5 commands, but it will be limited in its use for doing math in Maple.
The AI lacks resourcefulness and knowledge to replace a human as well.

I don't see it happening yet here on Maple primes, that all questions for Maple will be answered by AI chatGPT.

Have asked chatGPT a question :
Can chatGPT be self-learning ?
ChatGPT
Yes, in a sense ChatGPT can be self-learning, albeit in a limited way. While the model itself does not evolve or learn in the traditional sense as humans do, it can be improved through new training with more data or refinement of algorithms. OpenAI, the company behind ChatGPT, can regularly update and refine the model based on feedback and new technological developments. These updates help ChatGPT provide increasingly better answers and adapt to changes in language and knowledge.  

Was working a while back on the complex numbers and the Riemann hypothesis here on the forum
Also was then trying to master programming procedures.
But let's see what the AI can help me clarify something with these topics.
Already used the AI with some math questions via chatGPT direct and did get some new insight then.