@Thomas Dean The maplet plotdevice is working well on our Linux server, both for 2D and 3D plots. All I can think of is a low-level problem with your graphics card or driver. Please try updating that; some vendor links are given in our FAQ list.

What is your Linux distribution?

This got fixed in Maple 2018, by the way.

I'm getting the expected space curve, in all attempts. Is the code snippet part of a larger worksheet, possibly including plotsetup(maplet)? If so, please upload it to MaplePrimes.

What happens if you run

plotsetup(default);

before?

I suppose you are running Linux, right? The "Picked up JAVA_TOOL_OPTIONS" message is harmless.

... using the green arrow-up button of the message editor.

Before investigating, let's get the input correct. There is one term missing in your code: y(x,t)*diff(y(x,t),x)

pdetest(y(x,t)=exact_sol(x,t),PDE,IBC) will then succeed.

In the definition of M, replace sqrt(N(N+1)) by sqrt(N*(N+1)) for a start. I think the remaining errors were covered by tomlieslie's answer.

@Jean-Michel Collard Thanks for your suggestions. I agree particularly about updating GMP. Probably it's just a typo, but Maple's GMP library is currently at 5.1.1; see kernelopts(gmpversion) to check.

@acer This shortcut was introduced in Maple 2019.2. One of my favourite changes. :-)

You wrote:

> I start Maple 2020 on windows 10. Run a script which takes 1-2 days to complete.
> During this time, I can't use that Maple at all, since it is busy.

What about opening the script in one tab and working in the other tabs (that you open before starting the script)?

I rarely see the need to launch separate sessions, and Maple 2020 is running all the time here, of course.

@acer You wrote:

> Perhaps it would help to think of error as a language keyword.

Yes. That's precisely why it is listed on the ?keyword help page.

@tomleslie That's right, and I suspect that the inconsistency was due to mistakes in setting up the equations. You will notice that some coefficients are close to algebraic numbers; try identify(sys) to find some. And the remaining float values satisfy simple relations as well. If we assign them as follows:

a := 2.82063786985032:
b := 1.82063786985032:
c := 2.78876614599445:
d := 0.03966097875175:
e := 0.968128276144127:
f := 0.031871723855875:

Then b = a-1, d = 2*sqrt(2)-c, f = 1-e. Furthermore, a-c+e  = 1, b+d+f = -1+2*sqrt(2); I stopped searching here. The OP will know the exact parameter values, and be able to fix the problem. This is much better than a purely numerical investigation.

@manon22lr This implicit solution cannot be turned into an explicit one. That is not a weakness of dsolve, but simply due to the appearance of y(t) inside both ln and arctan.

What you can obtain instead is a series expansion:

lambdaS:=dsolve(ivp,y(t),'series');
odetest(lambdaS,ivp,'series');
lambdaP:=convert(lambdaS,'polynom');

It reveals how a and eta impact the solution - which is hopefully useful for your parameter studies.

@manon22lr This implicit solution cannot be turned into an explicit one. It's not a weakness of dsolve, but simply because y(t) appears both inside ln and arctan.

What you can get is a series expansion as follows:

lambdaS:=dsolve(ivp,y(t),'series');
odetest(lambdaS,ivp,'series');
lambdaP:=convert(lambdaS,'polynom');

It reveals how a and eta impact the result - which should be useful for your further parameter studies.

I also like your worksheet (thumbs up), and I'm sure it was fun to create. However, entering all these equations and figuring out the details of the animation sequences can become tedious, in my opinion.

An alternative approach is MapleSim which (essentially) "knows" the component equations and lets you focus on the Physical Modeling. For multibody mechanisms, it generates the animation on-the-fly, and lets you export it into various video formats. Have you taken a look at the Jansen two-legs example (https://www.maplesoft.com/products/maplesim/ModelGallery/detail.aspx?id=153) in our Model Gallery?

@vv Here's another value resulting in a reducible polynomial: k=(475/2187)^2, found in a double loop over small numerators and denominators up to 10000 (not just squares, so it took some time)..

While the general answer to the OP's question is "no", there are still interesting cases that he could investigate.