Have you checked for backups?
Depending on how Maple is terminated there should be backups if the options are configured like this

I thought when odetest returns zero without assumptions then the tested solution is valid over the complex domain. In your example this is not the case.

The worring consequence is that plotting for a given parameter the solution of one of the "root ode"s (where the residual of the identical solution of the origianl ode is non zero) does not show an empty plot. For this reason, I am now also of the opinion that one should work with the odetest of the original ode.  There is a flaw in my reasoning that no assumptions are made when using PDEtools:-Solve that I would like to understand.

I always see the input window with Maple 2024.1 and standard GUI settings. The window is not moving. Same with Maple 2020. What do you use?

Did it look like this?

It took a while, then it worked.

Hnx said he cannot reply

@nm 

You also use exponentiation as I did in my verification. I would be interested if a knowledable user could comment on the exponexponentiation operation. Does it "cut of branches" or is it a general operation that can be done without any restrictions?

This is too complex for me.

@ecterrab 

Your answer clarifies allot. It describes in general how dsolve works and why there can be many solutions. I was looking for something like that.

My answer was only guess work, based on observations I made here and there. I did not delete it after sending when I saw your answer (to document at least where a user is right or wrong in his interpretation).

I would not have guessed to find something of interest in ?dsolve,setup. So I never consulted this page. Besides technical details I now can describe myself better as a curios standard user. However, this page rasies again the question about the difference between classificon methods, returned results and methods for ODE solving. More specifically, why is dAlembert not listed under "Methods for 1st order ODEs"? Should this be clear to the standard user?

Finally, some thoughts on PDETools. PDETools is mentionned (not only on the dsolve,setup page) in a way that it is a natural part of ODE solving. Many answers here in this forum use PDETools as well. Why should a standard user interested in ODE solving consult PDE librararies? I have not found an answer to it yet. For me, the use of PDETools sounds like a workarround for something that is not possible with ODETools. If a libraray function can be used for PDEs and for ODEs shouldn't it be part of a DETool package?

Anyway, exanding at bit more on how dsolve works and the existence of branched solutions (I doubt that many users are aware of this) could strenghten the educational aspect of Maple in the nontrivial domain of differential equations. Here Maple is my first point of reference since I want to use Maple to get solutions. The other way arround (studying ODEs with a textbook and then finding the right commands in Maple) does not make sense to me.

Maybe also of interest:

https://www.mapleprimes.com/posts/220633-DMS-Degrees-Minute-Seconds-To-Decimal-Conversion

Not clear what you want to simplify. You could combine the roots under certain assumptions.

combine(sqrt(2)*sqrt(a[5])/sqrt(a[4])) assuming (0 < a[5], 0 < a[4])

@Thomas Richard 

That works. The tricky bit is when the spacecurve is not an explicit function of time and generated by numerical integration. If I understand @mmcdara solution correctly, he solves a sequence of IVP where each solution generates the initial values for the subsequent IVP. Quite some coding required for numerical solutions.
Thank you

@mmcdara 

That is a step in the right direction. The colorsheme option is of value when the animation is stopped.
Thank you!

Nice examples. 

I played a bit with integration methods

Used for the plot above:

sol := dsolve({sys, x(0) = 1.1, y(0) = 1.1, z(0) = -0.01}, {x(t), y(t), z(t)}, numeric);
sol2 := dsolve({sys, x(0) = 1.1, y(0) = 1.1, z(0) = -0.01}, numeric, method=classical[foreuler],maxfun=100000);
p1:= odeplot(sol, [x(t), y(t), z(t)], t = 0 .. 50, axes = boxed, numpoints = 50000, labels = [x, y, z], title = "Thomas Attractor", color = red):
p2:=odeplot(sol2, [x(t), y(t), z(t)], t = 0 .. 50, axes = boxed, numpoints = 50000, labels = [x, y, z], title = "Thomas Attractor",color=blue):
plots:-display(p1,p2,title="rkf45 (red) vs. forward Euler (blue)");

Before the loop, try

interface(warnlevel=0)

After the loop you can set it back to 3.

@Ronan 

I have two Laptops connected via UBS docs to large monitors. My current observations have be made in this configuration. Can't say yet if this is also valid in laptop mode without mouse. I will have an eye on it next time I am traveling.

I have also enabled windows screen saver. That you don't see it fits to my observation.

Thanks for sharing this detail

 @rlopez @Carl Love 

I have found a way to disappear submenus: Power buton -> sleep

Interstingly, turning of by hibernation did not show the effect. Submenus did not dissapear.

Can some confirm that sleep triggers the effect? If so, developers should be informed.