I have a system of ODEs with parameters, p[i], and variables, x[i].

f := [
-p[1]*x[1]^2+x[2],
-2*p[1]^2*x[1]^3+2*p[1]*x[1]*x[2]+x[1]+1
];

associated with the innitial conditions:
[x[1](0) = p[2], x[2](0) = p[3]].

I am interested in sets of parameters where the solution x[1](t) is the same; if [p[1],p[2],p[3]] is associated with a solution x(p,t), and [ph[1],ph[2],ph[3]] is asociated with the solution x(ph,t); then x[1](p,t)=x[1](ph,t) for all t if and only if

[ph[1] = ph[1],
ph[2] = p[2],
ph[3] = -p[1]*p[2]^2+p[2]^2*ph[1]+p[3]]

i.e. ph[1] takes any real value, ph[2] takes the same values as p[2] and ph[3] takes a value determined by the original parameter vector and ph[1].

In a previous question it was demonstrated that x[2](ph,t)/x[2](p,t) rapidly converge on p[1] as t increases for a specific parameter vector that was given in the question (see graph below)

 

This raises the question does this limit generally hold?

I have struggled to do this in maple and I am suspicious of the answer i have got
i.e.
limit (x[2](ph,t)/x[2](p,t),t=infinity)=+/- infinity

My question is
+ when does a finite limit exist?
+ what is the finite limit?

 

Hello,

I would like to see if MAPLE fits our needs. In order to see that I would like to consider the example which is posted in H. Iwaniec :"Introduction to the spectral theory (...)" p. 36, that is as follows:

Suppose that you have a PDE as follows:

This PDE has the following point symmetries:

These differential operators are the representations of the following matrix algebra:

1. I would like to see the MAPLE commands, which give the algebra $v_1, v_2, v_3$ 

2. I would like to see those commands, which give you the algebra $v_1, v_2, v_3$ as a representation of $X_1, X_2, X_3$.

3. Given the algebra $v$ I would like to see the commands which give you the Laplace-Beltrami operator $\Delta_{LB}=y\partial_{xx} + y\partial_{yy}$

( P.s. sorry for the intransparent form, I do not know how to insert formulae in the comment.)

Thanks in advance.

G45073

possible to solve following equation with unknown parameter omega.

parameter constant.

I see before for one dimension ode this type equation was solved.

Now for 2d equation is possible?

can consider or I can send again.

Best

2d-2

Dear Maple users

I have a question about performing operations on a matrix and another one about retrieving information from a matrix. I am looking for the easiest (hopefully also the shortest) way to do it:

1. Given a matrix with several rows and columns. I want to permute the rows in such a way that the entries in a specific column are ordered (either ascending or decending as wished).

2. Given a matrix with several rows and columns. I want to count how many entries in a specific column are above a certain given fixed value.   

I am pretty sure some of you guys out there can do it in an elegant way. Examples will be appreciated.  

Regards,

Erik

Download evaluate_a_sum.mw

Why am I not able to use my MaplePrimes login credentials to login into MapleCloud?

Hello,

I am facing a problem to calculate the variable "al" in a equation like shown below.

fe := int(sqrt(1+(-5.557990765*sin(5.557990765*x)-7.3*cos(5.557990765*x)-5.6*sinh(5.557990765*x)+7.3*cosh(5.557990765*x))^2), x = 0 .. al) = .5

Is there any method in maple to solve it even through using numeric methods.

I'm forward to your response.

Thank you very much!

so i just went from a really old version of maple to a the newest one maple 2019 and at first glance it doesn't seem to work correctly please take a look at the picture maybe there is a toggle i missed or something of the sorts thanks you for your time 

Dear Users!

Hoped everything going fine with you. I constrcut the following code to construct the polynomials for any M1 and M2

printlevel := 2; M1 := 3; M2 := 3; nu := 1;
for k1 from 0 while k1 <= M1-1 do
for k2 from 0 while k2 <= M2-1 do
GP[k1+1, k2+1] := simplify(sum((-1)^(k1-i1)*GAMMA(k1+i1+2*nu)*GAMMA(nu+1/2)*x^i1*(sum((-1)^(k2-i2)*GAMMA(k2+i2+2*nu)*GAMMA(nu+1/2)*y^i2/(GAMMA(i2+nu+1/2)*factorial(k2-i2)*factorial(i2)*GAMMA(2*nu)), i2 = 0 .. k2))/(GAMMA(i1+nu+1/2)*factorial(k1-i1)*factorial(i1)*GAMMA(2*nu)), i1 = 0 .. k1))
end do end do;
I want to put this polynomials in a vector like
[GP[1,1]   GP[1,2]   GP[1,3]   GP[2,1]   GP[2,2]   GP[2,3]   GP[3,1]   GP[3,2]   GP[3,3]]
Similarlty I want to construct a vector having constants for any values of M1 and M2 like this
[a[1,1]   a[1,2]   a[1,3]   a[2,1]   a[2,2]   a[2,3]   a[3,1]   a[3,2]   a[3,3]]

In worksheet mode when me is writing my code, running code, evaluating is and can not work well with maple?

How can inactive  action? Because have to wait many times and is very boring for me.

This is a general question concerning the numerical method(s) used in fsolve.

How can I know what algorithm / method (secant, Newton, etc.) is used when the  fsolve routine is called?

Thank you!

A few months ago i completely lost one of my linux operating systems in a single line of commands I entered into the terminal, and at some point I want to utilize the StringTools package with commands like  RegSubs and RegMatch to output the matching strings that match for the current command line content in a linux terminal, so I will know before I hit the enter key how stupid it was of me to do so *prior* to hitting the enter key.

The part I have no idea about is the piping of the keyboard input  for a terminal window to the maple session that will output the strings matching as previously described. I'm sorry if this question is not very clear I will try clarify more this afternoon. 

I have a tough integral I'm trying to solve (see attatched code). Maple seems to be able to compute it if I instruct it to integrate by parts, however the solutions don't make sense. For example, if I differentiate the result I expect to get my original integrand, but I do not. Furthermore, depending on which function you choose as 'u' and which as 'dv' when integrating by parts yields different results.

071319_Integral.mw

The attatched code has four examples:

1) Definite integration by parts

2) Indefinite integration by parts

3) Indefinite integration by parts, alternate choice of 'u'

4) Definite integration by parts, alternate choice of 'u'

and after each indefinite integration, I differentiate the result to compare with the orginal integrand.

What is going on here?

The exclaimation mark as far as i know can be viewed as an instruction to maple to begin communicating with the host operating system in some way. I attempted to open cmd.exe in windows 10 by entering 

>!cmd

But was not successful in passing arguments with the intention they are to be interpreted by the command prompt as commands that should be executed once cmd.exe is open.

Another maple command, ssystem seems to accomodate all the basic purposes for opening a terminal of the host OS, but the examples only involve commands that will be understood by a linux terminal, not the windows command line. I have a number of linux virtual machines running on my windows system, would it be possible open a terminal in one of those from the maple installation on the host machine?

The Help pages says:

Import a Worksheet from XML
  Open an existing XML document as a worksheet to modify the content or to change its appearance.
1. From the File menu, select Open. The Open dialog appears.
Select the Maple Worksheet as XML file type.

Those instructions do NOT apply to Maple 2018 on a Mac (although I have verified they DO apply on a Windows machine.) No dialog appears.

My .mw file is 90% format information and thenbits and pieces of Maple code. Is there some way to just extract the maple stuff? The file is pretty long and cutting out the xml stuff is very time consuming.

Thanks,