@salim-barzani So this new example is different since you want to substitute the second derivative, so that won't resolve first deriavtives, as you found. But if you know the solution, why not just substitute it in earlier?

If you don't want alpha to be zero then don't solve for it. Then you will get the variables you solve for given in terms of alpha, which means alpha can be any value. But maybe you are OK with some interrelationships between the parameters in the ODE. Perhaps just solve without any variable and select out those you want. I think you have to play around here.

Dr.D-thanks.mw

@sand15 I agree with your general point. And yet, there often are solutions to the many equations in few variables that the OP finds. I didn't do any sort of analysis, but I suspect the reason is that the form of F has been chosen after some analysis that ensures there will be a high likelihood (guarantee?) that there will be solutions; evidently not all the equations are independent.

I'm not sure how you generated these equations but some apparently blank characters were strange. I fixed the syntax errors by deleting many blanks and reentering them. Now you need to properly specify the equations.

1. As the error message suggests, you need more pdes.
2. Why no BCS/ICS for X?
3. You want to calculate the derivatives in the table but haven't specified at what X and Z values these are at (X = 0.1? but Z = ?). Add spaces to the table values so we can see the individual numbers.

plume_work.mw

@janhardo There is a simple logic error in kwadratisch__solver_met_plots-_bereik-complex_ver_2_4-11-2025.mw that results in the following error.

GeneralQuadraticSolver(1, 8, 7, 2, 11, 12);

gives

=== SOLVING: x^2+8*x*y+7*y^2+2*x+11*y+12 = 0 ===
Discriminant D = 36
Type: DEGENERATE CASE
   GENERAL FORM: x^2+8*x*y+7*y^2+2*x+11*y+12 = 0
   *** USING MAPLE'S ISOLVE ***
   GENERAL SOLUTION: 

      {x = -28, y = 4}, {x = -6, y = 4}, {x = 2, y = -1}, 

        {x = 4, y = -1}

These are the correct solutions, but this is the hyperbola case and not the degenerate case (as the plot shows).

@janhardo As usual, your AI has based its procedure on mine (basic structure, many variable names the same, and the central key way of finding the symbolic exponents is identical) and it has added a bit, e.g., dealing with different types of exponents separately. I was aware that more tests might have to be done, e.g., what happens if the user passes a list or vector? It might be useful to give some test cases in which its performance is superior; at the moment the test cases give the same result as mine.

However it has misunderstood a bit, which leads to actual wrong results, which IMO is more serious. Try

Collect_ultimate(5*r^a, r);

which incorrectly gives

@Preben Alsholm These are all variations, of course. Side relations (and algsubs) give a different (better?) result for

sqrt(cos(x)-cos(x)^3);
simplify(%,{cos(x)^2=1-sin(x)^2});

whereas subs returns the expression unchanged.

@nm The default postscript driver from the old days does not use color. There is a "cps" driver for color, so the following modification of @sand15's workaround gives a .ps file that has a colored grid when I open it in acrobat pro.

plotsetup(cps, plotoutput = "C:/Users/dharr/Documents/test.ps", plotoptions = noborder):
p:=plot(x^3, x = -8 .. 8, color = "blue",axis=[gridlines=[10,color="red"]]):
g := seq(plot(y, x=-8..8, color=red), y=[seq](-500..500, 100)), seq(plot([[x, -500], [x, 500]], color=red), x=[seq](-8..8, 2)):
plots:-display(p, g);  

I thought to convert the plot to an image file then export the image file, to get around different driver issues. But

p:=plot(x^3, x = -8 .. 8, color = "blue",axis=[gridlines=[10,color="red"]]):
i:=convert(p,Image):
op(2,i);
ImageTools:-Write("C:/Users/dharr/Documents/test.png",i);

from cmaple outputs  1 .. 600, 1 .. 800, 1 .. 3, as the hfarray dimensions, 5662 as the bytes written and a plot with no gridlines. From a worksheet the dimensions are the same but 19684 bytes are written and the gridlines appear. cmaple also ignores the size option in plot, whereas in a worhsheet the image dimensions change according to size. I'm mystified by the interpretation of this.

@JP Howe Copying your commands to Maple.ini in a directory and then starting an existing Maple worksheet in the same directory (by double-clicking on it) successfully finds and runs the Maple.ini commands. packages() shows LinearAlgebra is loaded.

There are several places that Maple.ini can be (see the help page ?worksheet/reference/initialization), and these are searched in a specific order, so you want to check you don't have a left-over one in a higher priority location.

By the way, your time domain expression doesn't seem to correspond to your transformed expression.

Download transfer_fn.mw

This is hard to diagnose without seeing your workheet. Please upload it using the green up-arrow in the Mapleprimes editor, select the file, click upload and the click either insert link or insert content.

@JP Howe I'm happy to help. If evaluating forever, there will be a message "Evaluating..." that replaces "Ready" along the bottom edge of the window. Enjoy Maple 2025.

@Alfred_F I made some updates since you replied, so you may wish to download the new files. algadd now properly deals with the infinity point. I assumed you were looking for integer solutions, which is a fun application, but if you are happy with the general case of rational solutions, the transformation can be simplified slightly as noted in a comment in the Elliptic2 file.

p.s. I am dharr, not dharr 8722, the number is just my reputation, which changes over time.

@salim-barzani Yes, I saw you substituted alpha with beta in pde1 to get pde. But you are only testing if you found a solution to pde. If you find it is a solution to pde, you have solved a special case of pde1 where alpha and beta are equal. But you aren't testing pde1 so I dont understand what you expect or what you think is wrong.

@JP Howe So it is a version issue. It is not clear to me what "hangs" means. Sometimes when hitting "enter" on an input region nothing happens - the solution to that can be to run the whole worksheet using the !!! icon. Or deleting that region and reentering it.
Hangs could mean just evaluating forever?
Or perhaps Maple freezes up and has to be killed from the OS?

For that integral, Maple uses the VectorCalculus package, which is not necessary. VectorCalculus redefines many common operations (like int), so I would not load that package unless you really need it. Try deleting the with(VectorCalculus) line.

A couple of tips:

To find the length of a vector, you can use numelems() rather than MTM:-size().

You have a loop to set the small values in a vector to zero. Maple's fnormal() command can do this (on the whole vector or on a number).