@ecterrab I tried getting Physics Updates 783 from the cloud from within Maple 2020.1.1.

It stopped in the middle of the process as Tom Leslie described. I didn't wait for a crash.

Then I created the folder structure as you described. I went to
https://www.maplesoft.com/products/maple/features/physicsresearch.aspx
and downloaded the file Physics Updates_1598849555273.maple.
I put that file in the lib folder and the version.txt into the Physics Updates folder.
I didn't get or see the other 2 files and was actually sure something was wrong because of that long number on the .maple file.
OK then I copied the override_maple.txt file from Maple 2019.

Now it appears to work.
The uninstall_manifest.mtxt file from Maple 2019 I didn't copy, so I don't have that in 2020 at this time.


 

@Kitonum Your procedure P cannot handle constants of type name.
Here is a revised version.
 

restart;
interface(typesetting=extended);
###
P:=proc(ode)
  local idiff,t;
  idiff:=convert(indets(ode,specfunc(diff)),D);
  t:=op~(idiff);
  if numelems(t)<>1 then error "Only one independent variable allowed. Got %1", t end if; 
  t:=op(t);
  Typesetting:-Settings(usedot=false,prime=t,typesetprime=true);
  ode
end proc:
###
ode1:=diff(y(t),t$2)+a*diff(y(t),t)+y(t)= b*diff(z(t),t);
P(ode1);
ode2:=diff(y(t),t$2)+a*diff(y(s),s)+y(t)= b*diff(z(t),t)
P(ode2); # error by design

@acer 

With floatPi = false (my setting) I don't get any problems, but JacobiTheta3 is not evaluated.
With floatPi = true I get a loss of kernel connection for your worksheet and for edgar's as well.

@janhardo As dharr said I changed all the cases of the double quotes (") into % and corrected the obvious error in defining sys (twice), where x and y should be x(t) and y(t) (and always should). The worksheet worked in my Maple 2020.
If you are in fact using a release beginning with Maple V you should not replace " by %, but the t's on x and y have to be put into sys.

Thank you for this fascinating mechanism. Theo's last name is Jansen, not Jensen, according to Wikipedia. He is Dutch, not Danish as I had hoped.

@Arif Ullah khan In similar problems N has been a substitute for infinity. I suppose that is not the case here?

@Arif Ullah khan You give some partial results for gamma = 1 and rho = nu:
Yet your original values were:
para:={nu=3, gamma=10} and rho = 2.

@vv Your example doesn't really suggest that does it? The values at t = 0 for U and X are certainly different:

 

Download MaplePrimes20-08-15_ode_problem.mwMaplePrimes20-08-15_ode_problem.mw

@mmcdara I believe that your ode is unstable in the forward direction, i.e. as t -> infinity, but stable in the opposite direction.
If I'm right and you are interested in a solution on the finite interval t = 0..t0, then start the solution at t0.
Since you only know X and D(X) at 0 you could try use a shooting method.
But even if you succeed in find starting values (faking not knowing U) for a solution starting at t = t0 (t0 > 0), then that solution will only be good on t = 0..t0. Just try using X(t0) = U(t0) and D(X)(t0) = D(U)(t0) as your initial contions.
You get perfect results for t = 0..t0, but for t > t0 not so.
An example:
Here I chose t0 = 1 and plottet X(t) on 0..1.35:

@pik1432 It is easy to write down several ode systems all with equilibria coming from solving your algebraic equations.
Just multiply say 3 of these equations by minus 1 and the equilbria are the same, but the jacobian and its eigenvalues are not.
Thus stability here must refer to the solving method and obviously must refer to a numerical method as used by fsolve, not an exact as used by solve.
##################################################################################
A trivial one dimensional example is
diff(x(t),t) = x(t) which has jacobian 1 at the equilibrium x = 0 and eigenvalue 1: 0 is unstable.
diff(x(t),t) = -x(t) which has jacobian -1 at the equilibrium x = 0 and eigenvalue -1: 0 is stable.
Yet in both cases determining the equilibrium consists in solving the same basic equation x=0.
 

@pik1432 I forgot that I used expand on your f9n10 as I see that also acer does.

Apparently you are using some hidden code. That doesn't exactly help.

Are you using 2D input?
If so then don't.
Go to Tools/Options/Display/Input display.  Pick Maple Notation (i.e 1D).
Then still with the Options window open go to Interface/Default format for new worksheets. Pick Worksheet.
Now press the button Apply Globally.

Open a new worksheet. I hope you like it better. I do!

If you use solve instead you will get a solution.

You didn't succeed in attaching a file. Use the fat green arrow in the editor.