in a lot of equation i have this problem which they find a condition by comparing  the  equation regarding to term must have 3 condition but i don't know why he found just one condition how we can get condition from E8&E9

Download C1.mw

i want to change tmy ODE equation to systems, this procedure is called galilian transformation as i saw , and this is just for second order or we can used for 3rd order and up too ?

there is a lot of example which i know by hand but i want to write by maple

in this equation i solved without polar which is not shown well without polar specially when a=0 without polar if we solve this  and the other point are complex which not shown like a point in plot, except point (0,0) other not fine, but i want to solve by polar for finding  limit cycle the polar way are so usefull and also for some nonlinear system how i can  change the system to polar and find r* and theta* and plot them ?

polar.mw

i want to plot the function appear in P but there is a variable t which appear from variable which my system is depending on u,v and must v appear in my function instead of exponential so exponential contain the t variable  there is any way for fixing this?

Download p1-1.mw

it is apear by sign of taking derivative from equation and substitute in it the sign less zero is stable otherwise is unstable but i want to shown by graph like shown in graph

plot-stablity-1equation.mw

what is problem in here

Download remove.mw

when we do the linearization we do transfer the critical point to the orgin, i want see the plot of nonlinear system before the linearization and after linearization which is critical point is tranfered to orgin, also i try to find `conserved quantity` and make a good plot with the critical point shown in graph how i can do the linearization by maple, also  we  by hand when we solved we show that in new system when we give him variable we have to write for each new system  u=x-x[0] when is u is new system for linearization we need that or not? becuase result is not change when we take jacobian result is same !

Linearization.mw

i want plot a system of differential equation and do phaseportrait i did but when i want make it a little bit more clear and colorfull like rainbow when i find the C.Q i don't know how set the option for ploting?

e1.mw

i have a system but i don't know how i can plot chaotic or is need time for ploting or not ?

Has anyone else run into the following bug in the PolynomialTools package?

> PolynomialTools[PolynomialToPDE]([z*f], [z], [f]);

                            d
                           [-- f(z)]
                            dz

> PolynomialTools[PolynomialToPDE]([z[1]*f], [z[1]], [f]);

                           [f(z[1])]

I believe the first behavior is correct, but when I use subscripted variables, I get the second behavior for linear terms.  (Nonlinear terms appear to work correctly:

>  PolynomialTools[PolynomialToPDE]([z[1]^2*f], [z[1]], [f]);
                                2
                               d
                             [------ f(z[1])]
                                  2
                              dz[1]

I have observed this in Maple 2024.2 and previous versions.  Does anyone know if it's fixed in Maple 2025?  (I don't have access yet.)  Does anyone know a good workaround for polynomials with both linear and nonlinear terms?

Thanks!

----Josh

On my journey of discovery through the world of Maple, I would like to ask for help again:
How are the properties of variables and the indexing of sequences handled/determined? For this purpose, I chose an old problem from a challenging MO as an exercise and tried it in the attached file, which, of course, failed.

Download test.mw

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Regarding to this equation i want to do the same as paper did, but i am not sure how i can determine the both  point in plot and how thus point show effect of system of equation and  how find jacobian in the two different point  i think he find it in general but i think we have to find it for each one  of equalibriom point  or we just find in general .
thus plot also are emazing did he use special code in matlab or mathematica? there is some app for plot thus kind of phase portrait but they not like this this is must have a special code for plotting in matlab or mathematica

Download bi-1.mw

The attached problem is from a 1988 MO. It can be solved using complete induction, paper, and pencil, and with some effort, yields a simple answer. It's quite challenging to do by hand, but with "derive", it only takes three lines and a fraction of a second. Mow test.mw

Download test.mw

I can't do it with Maple because I'm doing something wrong again. Therefore, I'm asking for help.

Recently, I was surprised by the fact that it is not possible to create a table, where the values of entries are tables.

Toy example:

T1:=table(["1"=table(["first"=12, "second"=15]), "2"= table(["first"=9, "second"=7])]);

The code

T1["1"];

doesn't return table(["first"=12, "second"=15])

If table has lists in right-hand side

T1:=table(["1"=[12, 15], "2"= [9, 7]]);

all works properly.