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Flattening a Matrix...

Asked by: Harry Garst 269
matrix flatten
May 28 2025
2  6

I'm looking for a flatten procedure for matrices (without first having to convert the matrix to a list, flatten it, and finally convert it back).
In this example, I am trying to generalize the matrix R to higher dimensions (here a 3 by 3 matrix, denoted as A, is used). I'm using a function, denoted as g, to construct a matrix. Obviously, the function applies to each cell and therefore, each cell contains a matrix in the resulting matrix. A flatten command would solve the problem. As a work-around I reconstruct the matrix In this example, but that is hard to generalize to more dimensions (or not?)

> 

restart; kernelopts(version); interface(version); with(LinearAlgebra); with(combinat); interface(rtablesize = 16)

`Maple 2024.2, X86 64 WINDOWS, Oct 29 2024, Build ID 1872373`

  

`Standard Worksheet Interface, Maple 2024.2, Windows 11, October 29 2024 Build ID 1872373`

  

[10, 10]

 (1)
> 

Antidiagonal := proc (n) local Q, r, c; Q := Matrix(n, n); seq(seq(`if`(r+c = RowDimension(Q)+1, assign('Q[r, c]', 1), assign('Q[r, c]', 0)), r = 1 .. RowDimension(Q)), c = 1 .. ColumnDimension(Q)); return Q end proc
> 

A := Matrix(3, 3, symbol = a)
> 

R := `<,>`(`<|>`(Adjoint(A([2, 3], [2, 3])), -Adjoint(A([1, 3], [2, 3])), Adjoint(A([1, 2], [2, 3]))), `<|>`(-Adjoint(A([2, 3], [1, 3])), Adjoint(A([1, 3], [1, 3])), -Adjoint(A([1, 2], [1, 3]))), `<|>`(Adjoint(A([2, 3], [1, 2])), -Adjoint(A([1, 3], [1, 2])), Adjoint(A([1, 2], [1, 2]))))

Matrix(%id = 36893490582445267772)

 (2)
> 

U := choose(3, 2)

[[1, 2], [1, 3], [2, 3]]

 (3)
> 

g := proc (r, c) options operator, arrow; Adjoint((eval*A^%T)(U[c], U[r])) end proc

proc (r, c) options operator, arrow; LinearAlgebra:-Adjoint((eval(A^%T))(U[c], U[r])) end proc

 (4)
> 

Q := Matrix(3, g)

Matrix(%id = 36893490582395297788)

 (5)
> 

Q := Antidiagonal(3).Q.Antidiagonal(3)

Matrix(%id = 36893490582401641396)

 (6)
> 

U := `<,>`(`<|>`(Q[1, 1], Q[1, 2], Q[1, 3]), `<|>`(Q[2, 1], Q[2, 2], Q[2, 3]), `<|>`(Q[3, 1], Q[3, 2], Q[3, 3]))

Matrix(%id = 36893490582412939004)

 (7)
> 

R-Matrix(6, 6, [[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0], [0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1]]).U^%T.Matrix(6, 6, [[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0], [0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1]])

Matrix(%id = 36893490582417081876)

 (8)


Download Flatten_a_matrix.mw

Inconsistency between pdetest manual substitution...

Asked by: salim-barzani 1590
substitution pde differential-equations
May 27 2025
0  3

Hi everyone,

I've encountered something odd while working with Maple's pdetest function. When I manually evaluate my proposed solution using eval() followed by simplify(), I get the expected identity 0 = 0, which suggests the solution satisfies the PDE. However, when I test the same solution using pdetest, it doesn't return zero. This inconsistency has left me unsure whether my solution is actually valid or if I'm missing something.

Has anyone else experienced this kind of discrepancy? Could this be due to how pdetest handles derivatives or symbolic simplification internally?

Any insights or suggestions would be greatly appreciated!

Download pde-test.mw

BarChart-Statistics...

Asked by: jalal 435
statistics barchart
May 27 2025
0  2

Hi,

I try to creat an activity on Statistics, and I'm stuck on the bar chart, ( in the last part of my worksheet) with xi on the x-axis (Ox) and ni on the y-axis (Oy). I'm using the BarChart command, but it's not giving the expected result.

Ideas?

S4_Statistiques_Descriptives_AxeTravail_Complet.mw

How to plot a vector with units and one without un...

Asked by: FDS 195
May 21 2025
0  2

Dear Power Users,

This is probably a simple question for you but I am stuck. In the attached worksheet I would like to plot (the plot is called P5) a vector with units (mm) against a vector without units. This didn't work out, so I removed the units from the vector with units, and this plotted but after the conversion the numeric values are no longer in mm but inches. How can I correct this?

Thank you in advance for your time and willingness to help.

testSheetHorseShoe.mw

How Plotting function without singularity?...

Asked by: salim-barzani 1590
parameters plotting
May 20 2025
0  2

in some of my function i have a big problem which i can't plot thus function even i know what is the shape of plot, i have two type of ploting directly giving parameter and using explor but for this kind of plot we can't use explor so i have to give the function directly parameter but is wasting my time a lot and i can't get my plot even spending a days by changing parameter one by one, my questions is this how i can plot this kind of function without bieng a singular i need this function to be non singular is not importan about the parameter can be any number 
thanks for any help 

plots-long_term_.mw

the shape of plot must be like this but must have two of them 

Display a simple plane...

Asked by: Ronan 1341
3d plane plotting
May 18 2025
0  12

This seems rediculous to have to ask. I just want to display a plane. The plot is used in other plots so I gave it a name. I get "length of output exceed 1000000" and the plot does not display. I then have to "display" the plot name "display(plt0)" to see it. I had tried geom3d but found if infuriating, (maybe I am missing something there).

An I missing something simple here?

restart

NULL

with(plots)

pln := x-2*y+3*z

x-2*y+3*z

 (1)

NULL

display(implicitplot3d(pln, x = -3 .. 3, y = -3 .. 3, z = -3 .. 3, style = patchnogrid, transparency = .6))

  

NULL

NULL

plt0 := display(implicitplot3d(pln, x = -3 .. 3, y = -3 .. 3, z = -3 .. 3, style = patchnogrid, transparency = .6))

`[Length of output exceeds limit of 1000000]`

 (2)

display(plt0)

  

Intended use

NULL

Download 2025-05-18_Q_display_a_simple_plane.mw

There is any way for knowing which parameter are r...

Asked by: salim-barzani 1590
solve ode parameters
May 18 2025
1  0

I'm currently working on applying a specific method to solve a nonlinear equation. However, I've encountered a recurring issue: during the process, I often cannot determine certain parameters, which forces me to abandon the solution or switch to a different method. This has happened multiple times and is disrupting my goal of applying all intended methods consistently to a single equation.

In particular, I’m struggling to identify the correct parameters for U(ξ), which are essential for the solution. This challenge is not limited to one method I’ve faced similar problems in previous attempts, and I’m unsure why these parameters cannot be derived in some cases.

My question is: How can I manage this issue effectively? Is there a reliable way to predict or determine whether the necessary parameters will emerge correctly before fully applying a method?

I would greatly appreciate any insights or strategies you could share to help me handle this problem more systematically.

Thank you in advance for your support.

runing.mw

How can I simplify a symbolic number?...

Asked by: Saalehorizontale 55
simplify symbolic rootof
May 16 2025
1  8

Hey guys, 

I am solving big systems of equations and doing some other stuff with the results. So now I got two diffrent ways and it turns out, that the give back the same result but they present it in diffrent ways. So my quesion now is, how can I simplify a symbolic number to its shortest form. In my example you can see, that the diffrence of y_1 and y_2 is 0, so they describe the same number. However y_2 is a way more complicated expression. So here I know the easier expression, but what if I dont. What is the right command to force maple to find a simplier expression for y_2? I read about evala but its doent do the job as you can see in the attached file. I also tryd things like simplify, normal, expand but it didint worked out too. simplify_symbolic_numbers.mw

> 

restart; y_1 := RootOf(_Z^5-2*_Z^4+9*_Z^3-14*_Z^2+9*_Z-2, .4687 .. .4727); y_2 := 2*RootOf(2*_Z^5-9*_Z^4+14*_Z^3-9*_Z^2+2*_Z-1, 2.109 .. 2.118)^4-9*RootOf(2*_Z^5-9*_Z^4+14*_Z^3-9*_Z^2+2*_Z-1, 2.109 .. 2.118)^3+14*RootOf(2*_Z^5-9*_Z^4+14*_Z^3-9*_Z^2+2*_Z-1, 2.109 .. 2.118)^2-9*RootOf(2*_Z^5-9*_Z^4+14*_Z^3-9*_Z^2+2*_Z-1, 2.109 .. 2.118)+2; evala(Normal(y_1-y_2)); evala(y_2)

0

  

2*RootOf(2*_Z^5-9*_Z^4+14*_Z^3-9*_Z^2+2*_Z-1, 2.109 .. 2.118)^4-9*RootOf(2*_Z^5-9*_Z^4+14*_Z^3-9*_Z^2+2*_Z-1, 2.109 .. 2.118)^3+14*RootOf(2*_Z^5-9*_Z^4+14*_Z^3-9*_Z^2+2*_Z-1, 2.109 .. 2.118)^2-9*RootOf(2*_Z^5-9*_Z^4+14*_Z^3-9*_Z^2+2*_Z-1, 2.109 .. 2.118)+2

 (1)
 

NULL

Download simplify_symbolic_numbers.mw

Thank you for your help. Regards, Felix

Identifying the Corresponding Solution Class for D...

Asked by: salim-barzani 1590
ode differential-equations duplicate-question
May 16 2025
2  2

I am working on obtaining the complete set of solutions for a given ordinary differential equation (ODE). While testing various cases from the auxiliary ODE method, I derived a solution of the form U(ξ). However, I am currently unable to determine which specific case or class from the established solution set this result corresponds to.

I would appreciate any guidance or method to correctly classify each obtained solution U(ξ) according to its respective case within the set of auxiliary ODE cases.

ode.mw

Guidance on replacement???...

Asked by: delvin 60
ode substitution differential-equations
May 16 2025
1  3

 Hi,

How can I replace all the expressions diff(G(xi), xi)/G(xi) with the new variable w(xi) in the next step? (Even the ones that have powers)

NULL

> 

eq2 := c*a0*(-lambda*diff(G(xi), xi) - mu*G(xi))/G(xi) - c*a0*diff(G(xi), xi)^2/G(xi)^2 - alpha*a0*diff(G(xi), xi)/((1 - 2*f(sqrt(lambda^2 - 4*mu)*y)*diff(G(xi), xi)/(sqrt(epsilon*lambda^2 - 4*epsilon*mu)*G(xi)) - f(sqrt(lambda^2 - 4*mu)*y)*lambda/sqrt(epsilon*lambda^2 - 4*epsilon*mu))*G(xi)) - alpha*a0*lambda/(2*(1 - 2*f(sqrt(lambda^2 - 4*mu)*y)*diff(G(xi), xi)/(sqrt(epsilon*lambda^2 - 4*epsilon*mu)*G(xi)) - f(sqrt(lambda^2 - 4*mu)*y)*lambda/sqrt(epsilon*lambda^2 - 4*epsilon*mu))) + alpha*a0*sqrt(epsilon*lambda^2 - 4*epsilon*mu)*epsilon*f(sqrt(lambda^2 - 4*mu)*y)/(2*(1 - 2*f(sqrt(lambda^2 - 4*mu)*y)*diff(G(xi), xi)/(sqrt(epsilon*lambda^2 - 4*epsilon*mu)*G(xi)) - f(sqrt(lambda^2 - 4*mu)*y)*lambda/sqrt(epsilon*lambda^2 - 4*epsilon*mu))) + alpha*a0*diff(G(xi), xi)/((1 + 2*f(sqrt(lambda^2 - 4*mu)*y)*diff(G(xi), xi)/(sqrt(epsilon*lambda^2 - 4*epsilon*mu)*G(xi)) + f(sqrt(lambda^2 - 4*mu)*y)*lambda/sqrt(epsilon*lambda^2 - 4*epsilon*mu))*G(xi)) + alpha*a0*lambda/(2*(1 + 2*f(sqrt(lambda^2 - 4*mu)*y)*diff(G(xi), xi)/(sqrt(epsilon*lambda^2 - 4*epsilon*mu)*G(xi)) + f(sqrt(lambda^2 - 4*mu)*y)*lambda/sqrt(epsilon*lambda^2 - 4*epsilon*mu))) + alpha*a0*sqrt(epsilon*lambda^2 - 4*epsilon*mu)*epsilon*f(sqrt(lambda^2 - 4*mu)*y)/(2*(1 + 2*f(sqrt(lambda^2 - 4*mu)*y)*diff(G(xi), xi)/(sqrt(epsilon*lambda^2 - 4*epsilon*mu)*G(xi)) + f(sqrt(lambda^2 - 4*mu)*y)*lambda/sqrt(epsilon*lambda^2 - 4*epsilon*mu))) - beta*a0^2*diff(G(xi), xi)^2/(G(xi)^2*(1 - 2*f(sqrt(lambda^2 - 4*mu)*y)*diff(G(xi), xi)/(sqrt(epsilon*lambda^2 - 4*epsilon*mu)*G(xi)) - f(sqrt(lambda^2 - 4*mu)*y)*lambda/sqrt(epsilon*lambda^2 - 4*epsilon*mu))) - beta*a0^2*diff(G(xi), xi)*lambda/(2*(1 - 2*f(sqrt(lambda^2 - 4*mu)*y)*diff(G(xi), xi)/(sqrt(epsilon*lambda^2 - 4*epsilon*mu)*G(xi)) - f(sqrt(lambda^2 - 4*mu)*y)*lambda/sqrt(epsilon*lambda^2 - 4*epsilon*mu))*G(xi)) + beta*a0^2*diff(G(xi), xi)*sqrt(epsilon*lambda^2 - 4*epsilon*mu)*epsilon*f(sqrt(lambda^2 - 4*mu)*y)/(2*(1 - 2*f(sqrt(lambda^2 - 4*mu)*y)*diff(G(xi), xi)/(sqrt(epsilon*lambda^2 - 4*epsilon*mu)*G(xi)) - f(sqrt(lambda^2 - 4*mu)*y)*lambda/sqrt(epsilon*lambda^2 - 4*epsilon*mu))*G(xi)) + beta*a0^2*diff(G(xi), xi)^2/(G(xi)^2*(1 + 2*f(sqrt(lambda^2 - 4*mu)*y)*diff(G(xi), xi)/(sqrt(epsilon*lambda^2 - 4*epsilon*mu)*G(xi)) + f(sqrt(lambda^2 - 4*mu)*y)*lambda/sqrt(epsilon*lambda^2 - 4*epsilon*mu))) + beta*a0^2*diff(G(xi), xi)*lambda/(2*(1 + 2*f(sqrt(lambda^2 - 4*mu)*y)*diff(G(xi), xi)/(sqrt(epsilon*lambda^2 - 4*epsilon*mu)*G(xi)) + f(sqrt(lambda^2 - 4*mu)*y)*lambda/sqrt(epsilon*lambda^2 - 4*epsilon*mu))*G(xi)) + beta*a0^2*diff(G(xi), xi)*sqrt(epsilon*lambda^2 - 4*epsilon*mu)*epsilon*f(sqrt(lambda^2 - 4*mu)*y)/(2*(1 + 2*f(sqrt(lambda^2 - 4*mu)*y)*diff(G(xi), xi)/(sqrt(epsilon*lambda^2 - 4*epsilon*mu)*G(xi)) + f(sqrt(lambda^2 - 4*mu)*y)*lambda/sqrt(epsilon*lambda^2 - 4*epsilon*mu))*G(xi)) - gamma*a0^3*diff(G(xi), xi)^3/(G(xi)^3*(1 - 2*f(sqrt(lambda^2 - 4*mu)*y)*diff(G(xi), xi)/(sqrt(epsilon*lambda^2 - 4*epsilon*mu)*G(xi)) - f(sqrt(lambda^2 - 4*mu)*y)*lambda/sqrt(epsilon*lambda^2 - 4*epsilon*mu))) - gamma*a0^3*diff(G(xi), xi)^2*lambda/(2*G(xi)^2*(1 - 2*f(sqrt(lambda^2 - 4*mu)*y)*diff(G(xi), xi)/(sqrt(epsilon*lambda^2 - 4*epsilon*mu)*G(xi)) - f(sqrt(lambda^2 - 4*mu)*y)*lambda/sqrt(epsilon*lambda^2 - 4*epsilon*mu))) + gamma*a0^3*diff(G(xi), xi)^2*sqrt(epsilon*lambda^2 - 4*epsilon*mu)*epsilon*f(sqrt(lambda^2 - 4*mu)*y)/(2*G(xi)^2*(1 - 2*f(sqrt(lambda^2 - 4*mu)*y)*diff(G(xi), xi)/(sqrt(epsilon*lambda^2 - 4*epsilon*mu)*G(xi)) - f(sqrt(lambda^2 - 4*mu)*y)*lambda/sqrt(epsilon*lambda^2 - 4*epsilon*mu))) + gamma*a0^3*diff(G(xi), xi)^3/(G(xi)^3*(1 + 2*f(sqrt(lambda^2 - 4*mu)*y)*diff(G(xi), xi)/(sqrt(epsilon*lambda^2 - 4*epsilon*mu)*G(xi)) + f(sqrt(lambda^2 - 4*mu)*y)*lambda/sqrt(epsilon*lambda^2 - 4*epsilon*mu))) + gamma*a0^3*diff(G(xi), xi)^2*lambda/(2*G(xi)^2*(1 + 2*f(sqrt(lambda^2 - 4*mu)*y)*diff(G(xi), xi)/(sqrt(epsilon*lambda^2 - 4*epsilon*mu)*G(xi)) + f(sqrt(lambda^2 - 4*mu)*y)*lambda/sqrt(epsilon*lambda^2 - 4*epsilon*mu))) + gamma*a0^3*diff(G(xi), xi)^2*sqrt(epsilon*lambda^2 - 4*epsilon*mu)*epsilon*f(sqrt(lambda^2 - 4*mu)*y)/(2*G(xi)^2*(1 + 2*f(sqrt(lambda^2 - 4*mu)*y)*diff(G(xi), xi)/(sqrt(epsilon*lambda^2 - 4*epsilon*mu)*G(xi)) + f(sqrt(lambda^2 - 4*mu)*y)*lambda/sqrt(epsilon*lambda^2 - 4*epsilon*mu)));

c*a0*(-lambda*(diff(G(xi), xi))-mu*G(xi))/G(xi)-c*a0*(diff(G(xi), xi))^2/G(xi)^2-alpha*a0*(diff(G(xi), xi))/((1-2*f((lambda^2-4*mu)^(1/2)*y)*(diff(G(xi), xi))/((epsilon*lambda^2-4*epsilon*mu)^(1/2)*G(xi))-f((lambda^2-4*mu)^(1/2)*y)*lambda/(epsilon*lambda^2-4*epsilon*mu)^(1/2))*G(xi))-alpha*a0*lambda/(2-4*f((lambda^2-4*mu)^(1/2)*y)*(diff(G(xi), xi))/((epsilon*lambda^2-4*epsilon*mu)^(1/2)*G(xi))-2*f((lambda^2-4*mu)^(1/2)*y)*lambda/(epsilon*lambda^2-4*epsilon*mu)^(1/2))+alpha*a0*(epsilon*lambda^2-4*epsilon*mu)^(1/2)*epsilon*f((lambda^2-4*mu)^(1/2)*y)/(2-4*f((lambda^2-4*mu)^(1/2)*y)*(diff(G(xi), xi))/((epsilon*lambda^2-4*epsilon*mu)^(1/2)*G(xi))-2*f((lambda^2-4*mu)^(1/2)*y)*lambda/(epsilon*lambda^2-4*epsilon*mu)^(1/2))+alpha*a0*(diff(G(xi), xi))/((1+2*f((lambda^2-4*mu)^(1/2)*y)*(diff(G(xi), xi))/((epsilon*lambda^2-4*epsilon*mu)^(1/2)*G(xi))+f((lambda^2-4*mu)^(1/2)*y)*lambda/(epsilon*lambda^2-4*epsilon*mu)^(1/2))*G(xi))+alpha*a0*lambda/(2+4*f((lambda^2-4*mu)^(1/2)*y)*(diff(G(xi), xi))/((epsilon*lambda^2-4*epsilon*mu)^(1/2)*G(xi))+2*f((lambda^2-4*mu)^(1/2)*y)*lambda/(epsilon*lambda^2-4*epsilon*mu)^(1/2))+alpha*a0*(epsilon*lambda^2-4*epsilon*mu)^(1/2)*epsilon*f((lambda^2-4*mu)^(1/2)*y)/(2+4*f((lambda^2-4*mu)^(1/2)*y)*(diff(G(xi), xi))/((epsilon*lambda^2-4*epsilon*mu)^(1/2)*G(xi))+2*f((lambda^2-4*mu)^(1/2)*y)*lambda/(epsilon*lambda^2-4*epsilon*mu)^(1/2))-beta*a0^2*(diff(G(xi), xi))^2/(G(xi)^2*(1-2*f((lambda^2-4*mu)^(1/2)*y)*(diff(G(xi), xi))/((epsilon*lambda^2-4*epsilon*mu)^(1/2)*G(xi))-f((lambda^2-4*mu)^(1/2)*y)*lambda/(epsilon*lambda^2-4*epsilon*mu)^(1/2)))-(1/2)*beta*a0^2*(diff(G(xi), xi))*lambda/((1-2*f((lambda^2-4*mu)^(1/2)*y)*(diff(G(xi), xi))/((epsilon*lambda^2-4*epsilon*mu)^(1/2)*G(xi))-f((lambda^2-4*mu)^(1/2)*y)*lambda/(epsilon*lambda^2-4*epsilon*mu)^(1/2))*G(xi))+(1/2)*beta*a0^2*(diff(G(xi), xi))*(epsilon*lambda^2-4*epsilon*mu)^(1/2)*epsilon*f((lambda^2-4*mu)^(1/2)*y)/((1-2*f((lambda^2-4*mu)^(1/2)*y)*(diff(G(xi), xi))/((epsilon*lambda^2-4*epsilon*mu)^(1/2)*G(xi))-f((lambda^2-4*mu)^(1/2)*y)*lambda/(epsilon*lambda^2-4*epsilon*mu)^(1/2))*G(xi))+beta*a0^2*(diff(G(xi), xi))^2/(G(xi)^2*(1+2*f((lambda^2-4*mu)^(1/2)*y)*(diff(G(xi), xi))/((epsilon*lambda^2-4*epsilon*mu)^(1/2)*G(xi))+f((lambda^2-4*mu)^(1/2)*y)*lambda/(epsilon*lambda^2-4*epsilon*mu)^(1/2)))+(1/2)*beta*a0^2*(diff(G(xi), xi))*lambda/((1+2*f((lambda^2-4*mu)^(1/2)*y)*(diff(G(xi), xi))/((epsilon*lambda^2-4*epsilon*mu)^(1/2)*G(xi))+f((lambda^2-4*mu)^(1/2)*y)*lambda/(epsilon*lambda^2-4*epsilon*mu)^(1/2))*G(xi))+(1/2)*beta*a0^2*(diff(G(xi), xi))*(epsilon*lambda^2-4*epsilon*mu)^(1/2)*epsilon*f((lambda^2-4*mu)^(1/2)*y)/((1+2*f((lambda^2-4*mu)^(1/2)*y)*(diff(G(xi), xi))/((epsilon*lambda^2-4*epsilon*mu)^(1/2)*G(xi))+f((lambda^2-4*mu)^(1/2)*y)*lambda/(epsilon*lambda^2-4*epsilon*mu)^(1/2))*G(xi))-gamma*a0^3*(diff(G(xi), xi))^3/(G(xi)^3*(1-2*f((lambda^2-4*mu)^(1/2)*y)*(diff(G(xi), xi))/((epsilon*lambda^2-4*epsilon*mu)^(1/2)*G(xi))-f((lambda^2-4*mu)^(1/2)*y)*lambda/(epsilon*lambda^2-4*epsilon*mu)^(1/2)))-(1/2)*gamma*a0^3*(diff(G(xi), xi))^2*lambda/(G(xi)^2*(1-2*f((lambda^2-4*mu)^(1/2)*y)*(diff(G(xi), xi))/((epsilon*lambda^2-4*epsilon*mu)^(1/2)*G(xi))-f((lambda^2-4*mu)^(1/2)*y)*lambda/(epsilon*lambda^2-4*epsilon*mu)^(1/2)))+(1/2)*gamma*a0^3*(diff(G(xi), xi))^2*(epsilon*lambda^2-4*epsilon*mu)^(1/2)*epsilon*f((lambda^2-4*mu)^(1/2)*y)/(G(xi)^2*(1-2*f((lambda^2-4*mu)^(1/2)*y)*(diff(G(xi), xi))/((epsilon*lambda^2-4*epsilon*mu)^(1/2)*G(xi))-f((lambda^2-4*mu)^(1/2)*y)*lambda/(epsilon*lambda^2-4*epsilon*mu)^(1/2)))+gamma*a0^3*(diff(G(xi), xi))^3/(G(xi)^3*(1+2*f((lambda^2-4*mu)^(1/2)*y)*(diff(G(xi), xi))/((epsilon*lambda^2-4*epsilon*mu)^(1/2)*G(xi))+f((lambda^2-4*mu)^(1/2)*y)*lambda/(epsilon*lambda^2-4*epsilon*mu)^(1/2)))+(1/2)*gamma*a0^3*(diff(G(xi), xi))^2*lambda/(G(xi)^2*(1+2*f((lambda^2-4*mu)^(1/2)*y)*(diff(G(xi), xi))/((epsilon*lambda^2-4*epsilon*mu)^(1/2)*G(xi))+f((lambda^2-4*mu)^(1/2)*y)*lambda/(epsilon*lambda^2-4*epsilon*mu)^(1/2)))+(1/2)*gamma*a0^3*(diff(G(xi), xi))^2*(epsilon*lambda^2-4*epsilon*mu)^(1/2)*epsilon*f((lambda^2-4*mu)^(1/2)*y)/(G(xi)^2*(1+2*f((lambda^2-4*mu)^(1/2)*y)*(diff(G(xi), xi))/((epsilon*lambda^2-4*epsilon*mu)^(1/2)*G(xi))+f((lambda^2-4*mu)^(1/2)*y)*lambda/(epsilon*lambda^2-4*epsilon*mu)^(1/2)))

 (1)

NULL

Download 123.mw

Page print formating problem Maple 2024...

Asked by: Ronan 1341
pdf export table
May 15 2025
0  3

I have a print format problem in Maple 2024.  For documents I print out, I use a special layout where all the contents are inside a table. The table is rigged to print on A4 paper. This is useful for my math notes. I havent done this for 18+ months. There appears to be a bug in Maple 2024. Only the first page is printed. Things work ok in Maple 2023. Maybe it is a setting difference or corruption in my install. Could somebody confirm this. Also if you can reproduce the problem could you let me know if it is in Maple 2025. I haven't upgraded yet.

 

2025-05-15_Q_page_print_formating.mw 
2025-05-15_Q_page_print_formating_M_2023.pdf
2025-05-15_Q_page_print_formating_M_2024.pdf

how to find posint solution of a specified equatio...

Asked by: Aixleft math 120
factorial
May 15 2025
0  4

Hi! how to find posint solution of this equation?

Is factorial move fast so that cannot solve?

any advice is appreciated.

> 

restart
> 

NULL
> 

eq := `assuming`([factorial(x)+1 = y^2], [x::posint, y::posint])

factorial(x)+1 = y^2

 (1)
> 

`assuming`([solve(eq, {x, y})], [x <= 100, y <= 100])

{x = RootOf(factorial(_Z)-y^2+1), y = y}

 (2)
 

NULL

Download find_posint_.mw

how to decompose a rational fraction into simple...

Asked by: Blanc 20
modp rational-function edited-question
May 12 2025
1  13

Hello,
Can you tell me how to decompose a rational fraction into simple elements in Fp?

Thank you.

How determine number of condition and inf it then ...

Asked by: salim-barzani 1590
ode substitution differential-equations
May 09 2025
3  1

i seperate my equation of real part and imaginary part i want  after taking integrale from my real part we see the pattern betwen real and imaginary part  which they equal about variable beside coefficient , i want to determine and find parameter from real part of my equation then substitute in imaginary for solving but  the number of condition i don't know is how much and there is a little bit repeatation how i can determine the correct one and then substitute ?

> 

restart
> 

with(PDEtools)
> 

undeclare(prime, quiet)
> 

declare(u(x, t), quiet); declare(U(xi), quiet); declare(V(xi), quiet)
> 

pde := I*(diff(u(x, t), `$`(t, 2))-s^2*(diff(u(x, t), `$`(x, 2))))+(1/24)*c[1]*(diff(u(x, t), t, `$`(x, 4)))-alpha*s*c[1]*(diff(u(x, t), `$`(x, 5)))+diff(c[2]*u(x, t)*U(-t*v+x)^2, t)-beta*s*(diff(c[2]*u(x, t)*U(-t*v+x)^2, x))

I*(diff(diff(u(x, t), t), t)-s^2*(diff(diff(u(x, t), x), x)))+(1/24)*c[1]*(diff(diff(diff(diff(diff(u(x, t), t), x), x), x), x))-alpha*s*c[1]*(diff(diff(diff(diff(diff(u(x, t), x), x), x), x), x))+c[2]*(diff(u(x, t), t))*U(-t*v+x)^2-2*c[2]*u(x, t)*U(-t*v+x)*(D(U))(-t*v+x)*v-beta*s*(c[2]*(diff(u(x, t), x))*U(-t*v+x)^2+2*c[2]*u(x, t)*U(-t*v+x)*(D(U))(-t*v+x))

 (1)
> 

G1 := U(-t*v+x) = U(xi); G2 := (D(U))(-t*v+x) = diff(U(xi), xi); G3 := ((D@@2)(U))(-t*v+x) = diff(U(xi), `$`(xi, 2)); G4 := ((D@@3)(U))(-t*v+x) = diff(U(xi), `$`(xi, 3)); G5 := ((D@@4)(U))(-t*v+x) = diff(U(xi), `$`(xi, 4)); G6 := ((D@@5)(U))(-t*v+x) = diff(U(xi), `$`(xi, 5))
> 

T := xi = -t*v+x; T1 := u(x, t) = U(-t*v+x)*exp(I*k*(t*w+x))

xi = -t*v+x

  

u(x, t) = U(-t*v+x)*exp(I*k*(t*w+x))

 (2)
> 

P1 := I*(diff(u(x, t), `$`(t, 2))-s^2*(diff(u(x, t), `$`(x, 2))))+(1/24)*c[1]*(diff(u(x, t), t, `$`(x, 4)))-alpha*s*c[1]*(diff(u(x, t), `$`(x, 5)))+diff(c[2]*u(x, t)*U(-t*v+x)^2, t)-beta*s*(diff(c[2]*u(x, t)*U(-t*v+x)^2, x))

I*(diff(diff(u(x, t), t), t)-s^2*(diff(diff(u(x, t), x), x)))+(1/24)*c[1]*(diff(diff(diff(diff(diff(u(x, t), t), x), x), x), x))-alpha*s*c[1]*(diff(diff(diff(diff(diff(u(x, t), x), x), x), x), x))+c[2]*(diff(u(x, t), t))*U(-t*v+x)^2-2*c[2]*u(x, t)*U(-t*v+x)*(D(U))(-t*v+x)*v-beta*s*(c[2]*(diff(u(x, t), x))*U(-t*v+x)^2+2*c[2]*u(x, t)*U(-t*v+x)*(D(U))(-t*v+x))

 (3)
> 

P11 := eval(P1, {T, T1})

I*(((D@@2)(U))(-t*v+x)*v^2*exp(I*k*(t*w+x))-(2*I)*(D(U))(-t*v+x)*v*k*w*exp(I*k*(t*w+x))-U(-t*v+x)*k^2*w^2*exp(I*k*(t*w+x))-s^2*(((D@@2)(U))(-t*v+x)*exp(I*k*(t*w+x))+(2*I)*(D(U))(-t*v+x)*k*exp(I*k*(t*w+x))-U(-t*v+x)*k^2*exp(I*k*(t*w+x))))+(1/24)*c[1]*(-((D@@5)(U))(-t*v+x)*v*exp(I*k*(t*w+x))+(4*I)*((D@@2)(U))(-t*v+x)*v*k^3*exp(I*k*(t*w+x))+I*U(-t*v+x)*k^5*w*exp(I*k*(t*w+x))+6*((D@@3)(U))(-t*v+x)*v*k^2*exp(I*k*(t*w+x))-(4*I)*((D@@4)(U))(-t*v+x)*v*k*exp(I*k*(t*w+x))-(6*I)*((D@@2)(U))(-t*v+x)*k^3*w*exp(I*k*(t*w+x))-(D(U))(-t*v+x)*v*k^4*exp(I*k*(t*w+x))+I*((D@@4)(U))(-t*v+x)*k*w*exp(I*k*(t*w+x))-4*((D@@3)(U))(-t*v+x)*k^2*w*exp(I*k*(t*w+x))+4*(D(U))(-t*v+x)*k^4*w*exp(I*k*(t*w+x)))-alpha*s*c[1]*(((D@@5)(U))(-t*v+x)*exp(I*k*(t*w+x))+(5*I)*((D@@4)(U))(-t*v+x)*k*exp(I*k*(t*w+x))-10*((D@@3)(U))(-t*v+x)*k^2*exp(I*k*(t*w+x))-(10*I)*((D@@2)(U))(-t*v+x)*k^3*exp(I*k*(t*w+x))+5*(D(U))(-t*v+x)*k^4*exp(I*k*(t*w+x))+I*U(-t*v+x)*k^5*exp(I*k*(t*w+x)))+c[2]*(-(D(U))(-t*v+x)*v*exp(I*k*(t*w+x))+I*U(-t*v+x)*k*w*exp(I*k*(t*w+x)))*U(-t*v+x)^2-2*c[2]*U(-t*v+x)^2*exp(I*k*(t*w+x))*(D(U))(-t*v+x)*v-beta*s*(c[2]*((D(U))(-t*v+x)*exp(I*k*(t*w+x))+I*U(-t*v+x)*k*exp(I*k*(t*w+x)))*U(-t*v+x)^2+2*c[2]*U(-t*v+x)^2*exp(I*k*(t*w+x))*(D(U))(-t*v+x))

 (4)
> 

P111 := subs({G1, G2, G3, G4, G5, G6}, P11)

I*((diff(diff(U(xi), xi), xi))*v^2*exp(I*k*(t*w+x))-(2*I)*(diff(U(xi), xi))*v*k*w*exp(I*k*(t*w+x))-U(xi)*k^2*w^2*exp(I*k*(t*w+x))-s^2*((diff(diff(U(xi), xi), xi))*exp(I*k*(t*w+x))+(2*I)*(diff(U(xi), xi))*k*exp(I*k*(t*w+x))-U(xi)*k^2*exp(I*k*(t*w+x))))+(1/24)*c[1]*(-(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*v*exp(I*k*(t*w+x))+(4*I)*(diff(diff(U(xi), xi), xi))*v*k^3*exp(I*k*(t*w+x))+I*U(xi)*k^5*w*exp(I*k*(t*w+x))+6*(diff(diff(diff(U(xi), xi), xi), xi))*v*k^2*exp(I*k*(t*w+x))-(4*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*v*k*exp(I*k*(t*w+x))-(6*I)*(diff(diff(U(xi), xi), xi))*k^3*w*exp(I*k*(t*w+x))-(diff(U(xi), xi))*v*k^4*exp(I*k*(t*w+x))+I*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k*w*exp(I*k*(t*w+x))-4*(diff(diff(diff(U(xi), xi), xi), xi))*k^2*w*exp(I*k*(t*w+x))+4*(diff(U(xi), xi))*k^4*w*exp(I*k*(t*w+x)))-alpha*s*c[1]*((diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*exp(I*k*(t*w+x))+(5*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k*exp(I*k*(t*w+x))-10*(diff(diff(diff(U(xi), xi), xi), xi))*k^2*exp(I*k*(t*w+x))-(10*I)*(diff(diff(U(xi), xi), xi))*k^3*exp(I*k*(t*w+x))+5*(diff(U(xi), xi))*k^4*exp(I*k*(t*w+x))+I*U(xi)*k^5*exp(I*k*(t*w+x)))+c[2]*(-(diff(U(xi), xi))*v*exp(I*k*(t*w+x))+I*U(xi)*k*w*exp(I*k*(t*w+x)))*U(xi)^2-2*c[2]*U(xi)^2*exp(I*k*(t*w+x))*(diff(U(xi), xi))*v-beta*s*(c[2]*((diff(U(xi), xi))*exp(I*k*(t*w+x))+I*U(xi)*k*exp(I*k*(t*w+x)))*U(xi)^2+2*c[2]*U(xi)^2*exp(I*k*(t*w+x))*(diff(U(xi), xi)))

 (5)
> 

pde1 := P111 = 0

I*((diff(diff(U(xi), xi), xi))*v^2*exp(I*k*(t*w+x))-(2*I)*(diff(U(xi), xi))*v*k*w*exp(I*k*(t*w+x))-U(xi)*k^2*w^2*exp(I*k*(t*w+x))-s^2*((diff(diff(U(xi), xi), xi))*exp(I*k*(t*w+x))+(2*I)*(diff(U(xi), xi))*k*exp(I*k*(t*w+x))-U(xi)*k^2*exp(I*k*(t*w+x))))+(1/24)*c[1]*(-(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*v*exp(I*k*(t*w+x))+(4*I)*(diff(diff(U(xi), xi), xi))*v*k^3*exp(I*k*(t*w+x))+I*U(xi)*k^5*w*exp(I*k*(t*w+x))+6*(diff(diff(diff(U(xi), xi), xi), xi))*v*k^2*exp(I*k*(t*w+x))-(4*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*v*k*exp(I*k*(t*w+x))-(6*I)*(diff(diff(U(xi), xi), xi))*k^3*w*exp(I*k*(t*w+x))-(diff(U(xi), xi))*v*k^4*exp(I*k*(t*w+x))+I*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k*w*exp(I*k*(t*w+x))-4*(diff(diff(diff(U(xi), xi), xi), xi))*k^2*w*exp(I*k*(t*w+x))+4*(diff(U(xi), xi))*k^4*w*exp(I*k*(t*w+x)))-alpha*s*c[1]*((diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*exp(I*k*(t*w+x))+(5*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k*exp(I*k*(t*w+x))-10*(diff(diff(diff(U(xi), xi), xi), xi))*k^2*exp(I*k*(t*w+x))-(10*I)*(diff(diff(U(xi), xi), xi))*k^3*exp(I*k*(t*w+x))+5*(diff(U(xi), xi))*k^4*exp(I*k*(t*w+x))+I*U(xi)*k^5*exp(I*k*(t*w+x)))+c[2]*(-(diff(U(xi), xi))*v*exp(I*k*(t*w+x))+I*U(xi)*k*w*exp(I*k*(t*w+x)))*U(xi)^2-2*c[2]*U(xi)^2*exp(I*k*(t*w+x))*(diff(U(xi), xi))*v-beta*s*(c[2]*((diff(U(xi), xi))*exp(I*k*(t*w+x))+I*U(xi)*k*exp(I*k*(t*w+x)))*U(xi)^2+2*c[2]*U(xi)^2*exp(I*k*(t*w+x))*(diff(U(xi), xi))) = 0

 (6)
> 

numer(lhs(pde1))*denom(rhs(pde1)) = numer(rhs(pde1))*denom(lhs(pde1))

-exp(I*k*(t*w+x))*((diff(U(xi), xi))*k^4*v*c[1]-4*(diff(U(xi), xi))*k^4*w*c[1]-48*(diff(U(xi), xi))*k*v*w+72*c[2]*U(xi)^2*(diff(U(xi), xi))*v-6*(diff(diff(diff(U(xi), xi), xi), xi))*k^2*v*c[1]+4*(diff(diff(diff(U(xi), xi), xi), xi))*k^2*w*c[1]+24*(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*alpha*s*c[1]-(24*I)*U(xi)*k^2*s^2+(24*I)*U(xi)*k^2*w^2+(24*I)*U(xi)*alpha*k^5*s*c[1]-(240*I)*(diff(diff(U(xi), xi), xi))*alpha*k^3*s*c[1]+(24*I)*U(xi)^3*beta*k*s*c[2]+(120*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*alpha*k*s*c[1]+120*(diff(U(xi), xi))*alpha*k^4*s*c[1]+72*(diff(U(xi), xi))*U(xi)^2*beta*s*c[2]-240*(diff(diff(diff(U(xi), xi), xi), xi))*alpha*k^2*s*c[1]-I*U(xi)*k^5*w*c[1]-(4*I)*(diff(diff(U(xi), xi), xi))*k^3*v*c[1]+(6*I)*(diff(diff(U(xi), xi), xi))*k^3*w*c[1]-(24*I)*U(xi)^3*k*w*c[2]+(4*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k*v*c[1]-I*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k*w*c[1]-48*(diff(U(xi), xi))*k*s^2+(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*v*c[1]+(24*I)*(diff(diff(U(xi), xi), xi))*s^2-(24*I)*(diff(diff(U(xi), xi), xi))*v^2) = 0

 (7)
> 

%/(-exp(I*k*(t*w+x)))

(diff(U(xi), xi))*k^4*v*c[1]-4*(diff(U(xi), xi))*k^4*w*c[1]-48*(diff(U(xi), xi))*k*v*w+72*c[2]*U(xi)^2*(diff(U(xi), xi))*v-6*(diff(diff(diff(U(xi), xi), xi), xi))*k^2*v*c[1]+4*(diff(diff(diff(U(xi), xi), xi), xi))*k^2*w*c[1]+24*(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*alpha*s*c[1]-(24*I)*U(xi)*k^2*s^2+(24*I)*U(xi)*k^2*w^2+(24*I)*U(xi)*alpha*k^5*s*c[1]-(240*I)*(diff(diff(U(xi), xi), xi))*alpha*k^3*s*c[1]+(24*I)*U(xi)^3*beta*k*s*c[2]+(120*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*alpha*k*s*c[1]+120*(diff(U(xi), xi))*alpha*k^4*s*c[1]+72*(diff(U(xi), xi))*U(xi)^2*beta*s*c[2]-240*(diff(diff(diff(U(xi), xi), xi), xi))*alpha*k^2*s*c[1]-I*U(xi)*k^5*w*c[1]-(4*I)*(diff(diff(U(xi), xi), xi))*k^3*v*c[1]+(6*I)*(diff(diff(U(xi), xi), xi))*k^3*w*c[1]-(24*I)*U(xi)^3*k*w*c[2]+(4*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k*v*c[1]-I*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k*w*c[1]-48*(diff(U(xi), xi))*k*s^2+(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*v*c[1]+(24*I)*(diff(diff(U(xi), xi), xi))*s^2-(24*I)*(diff(diff(U(xi), xi), xi))*v^2 = 0

 (8)
> 

Re(%)

Re((diff(U(xi), xi))*k^4*v*c[1]-4*(diff(U(xi), xi))*k^4*w*c[1]-48*(diff(U(xi), xi))*k*v*w+72*c[2]*U(xi)^2*(diff(U(xi), xi))*v-6*(diff(diff(diff(U(xi), xi), xi), xi))*k^2*v*c[1]+4*(diff(diff(diff(U(xi), xi), xi), xi))*k^2*w*c[1]+24*(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*alpha*s*c[1]+120*(diff(U(xi), xi))*alpha*k^4*s*c[1]+72*(diff(U(xi), xi))*U(xi)^2*beta*s*c[2]-240*(diff(diff(diff(U(xi), xi), xi), xi))*alpha*k^2*s*c[1]-48*(diff(U(xi), xi))*k*s^2+(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*v*c[1])-Im(-24*U(xi)*k^2*s^2+24*U(xi)*k^2*w^2+24*U(xi)*alpha*k^5*s*c[1]-240*(diff(diff(U(xi), xi), xi))*alpha*k^3*s*c[1]+24*U(xi)^3*beta*k*s*c[2]+120*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*alpha*k*s*c[1]-U(xi)*k^5*w*c[1]-4*(diff(diff(U(xi), xi), xi))*k^3*v*c[1]+6*(diff(diff(U(xi), xi), xi))*k^3*w*c[1]-24*U(xi)^3*k*w*c[2]+4*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k*v*c[1]-(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k*w*c[1]+24*(diff(diff(U(xi), xi), xi))*s^2-24*(diff(diff(U(xi), xi), xi))*v^2) = 0

 (9)
> 

R := (diff(U(xi), xi))*k^4*v*c[1]-4*(diff(U(xi), xi))*k^4*w*c[1]-48*(diff(U(xi), xi))*k*v*w+72*c[2]*U(xi)^2*(diff(U(xi), xi))*v-6*(diff(diff(diff(U(xi), xi), xi), xi))*k^2*v*c[1]+4*(diff(diff(diff(U(xi), xi), xi), xi))*k^2*w*c[1]+24*(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*alpha*s*c[1]+120*(diff(U(xi), xi))*alpha*k^4*s*c[1]+72*(diff(U(xi), xi))*U(xi)^2*beta*s*c[2]-240*(diff(diff(diff(U(xi), xi), xi), xi))*alpha*k^2*s*c[1]-48*(diff(U(xi), xi))*k*s^2+(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*v*c[1] = 0

(diff(U(xi), xi))*k^4*v*c[1]-4*(diff(U(xi), xi))*k^4*w*c[1]-48*(diff(U(xi), xi))*k*v*w+72*c[2]*U(xi)^2*(diff(U(xi), xi))*v-6*(diff(diff(diff(U(xi), xi), xi), xi))*k^2*v*c[1]+4*(diff(diff(diff(U(xi), xi), xi), xi))*k^2*w*c[1]+24*(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*alpha*s*c[1]+120*(diff(U(xi), xi))*alpha*k^4*s*c[1]+72*(diff(U(xi), xi))*U(xi)^2*beta*s*c[2]-240*(diff(diff(diff(U(xi), xi), xi), xi))*alpha*k^2*s*c[1]-48*(diff(U(xi), xi))*k*s^2+(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*v*c[1] = 0

 (10)
> 

collect(R, {U(xi), diff(U(xi), xi), diff(U(xi), `$`(xi, 3)), diff(diff(U(xi), xi), xi), diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi)})

(72*beta*s*c[2]+72*v*c[2])*(diff(U(xi), xi))*U(xi)^2+(120*alpha*k^4*s*c[1]+k^4*v*c[1]-4*k^4*w*c[1]-48*k*s^2-48*k*v*w)*(diff(U(xi), xi))+(-240*alpha*k^2*s*c[1]-6*k^2*v*c[1]+4*k^2*w*c[1])*(diff(diff(diff(U(xi), xi), xi), xi))+(24*alpha*s*c[1]+v*c[1])*(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi)) = 0

 (11)
> 

map(int, (72*beta*s*c[2]+72*v*c[2])*(diff(U(xi), xi))*U(xi)^2+(120*alpha*k^4*s*c[1]+k^4*v*c[1]-4*k^4*w*c[1]-48*k*s^2-48*k*v*w)*(diff(U(xi), xi))+(-240*alpha*k^2*s*c[1]-6*k^2*v*c[1]+4*k^2*w*c[1])*(diff(diff(diff(U(xi), xi), xi), xi))+(24*alpha*s*c[1]+v*c[1])*(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi)) = 0, xi)

(24*alpha*s*c[1]+v*c[1])*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))+(-240*alpha*k^2*s*c[1]-6*k^2*v*c[1]+4*k^2*w*c[1])*(diff(diff(U(xi), xi), xi))+(120*alpha*k^4*s*c[1]+k^4*v*c[1]-4*k^4*w*c[1]-48*k*s^2-48*k*v*w)*U(xi)+(1/3)*(72*beta*s*c[2]+72*v*c[2])*U(xi)^3 = 0

 (12)
> 

numer(lhs((24*alpha*s*c[1]+v*c[1])*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))+(-240*alpha*k^2*s*c[1]-6*k^2*v*c[1]+4*k^2*w*c[1])*(diff(diff(U(xi), xi), xi))+(120*alpha*k^4*s*c[1]+k^4*v*c[1]-4*k^4*w*c[1]-48*k*s^2-48*k*v*w)*U(xi)+(1/3)*(72*beta*s*c[2]+72*v*c[2])*U(xi)^3 = 0))*denom(rhs((24*alpha*s*c[1]+v*c[1])*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))+(-240*alpha*k^2*s*c[1]-6*k^2*v*c[1]+4*k^2*w*c[1])*(diff(diff(U(xi), xi), xi))+(120*alpha*k^4*s*c[1]+k^4*v*c[1]-4*k^4*w*c[1]-48*k*s^2-48*k*v*w)*U(xi)+(1/3)*(72*beta*s*c[2]+72*v*c[2])*U(xi)^3 = 0)) = numer(rhs((24*alpha*s*c[1]+v*c[1])*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))+(-240*alpha*k^2*s*c[1]-6*k^2*v*c[1]+4*k^2*w*c[1])*(diff(diff(U(xi), xi), xi))+(120*alpha*k^4*s*c[1]+k^4*v*c[1]-4*k^4*w*c[1]-48*k*s^2-48*k*v*w)*U(xi)+(1/3)*(72*beta*s*c[2]+72*v*c[2])*U(xi)^3 = 0))*denom(lhs((24*alpha*s*c[1]+v*c[1])*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))+(-240*alpha*k^2*s*c[1]-6*k^2*v*c[1]+4*k^2*w*c[1])*(diff(diff(U(xi), xi), xi))+(120*alpha*k^4*s*c[1]+k^4*v*c[1]-4*k^4*w*c[1]-48*k*s^2-48*k*v*w)*U(xi)+(1/3)*(72*beta*s*c[2]+72*v*c[2])*U(xi)^3 = 0))

120*U(xi)*alpha*k^4*s*c[1]+U(xi)*k^4*v*c[1]-4*U(xi)*k^4*w*c[1]-240*(diff(diff(U(xi), xi), xi))*alpha*k^2*s*c[1]+24*U(xi)^3*beta*s*c[2]-6*(diff(diff(U(xi), xi), xi))*k^2*v*c[1]+4*(diff(diff(U(xi), xi), xi))*k^2*w*c[1]+24*U(xi)^3*v*c[2]+24*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*alpha*s*c[1]-48*U(xi)*k*s^2-48*U(xi)*k*v*w+(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*v*c[1] = 0

 (13)
> 

RR := collect(%, {U(xi), diff(U(xi), xi), diff(U(xi), `$`(xi, 3)), diff(diff(U(xi), xi), xi), diff(diff(diff(diff(U(xi), xi), xi), xi), xi), diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi)})

(24*beta*s*c[2]+24*v*c[2])*U(xi)^3+(120*alpha*k^4*s*c[1]+k^4*v*c[1]-4*k^4*w*c[1]-48*k*s^2-48*k*v*w)*U(xi)+(-240*alpha*k^2*s*c[1]-6*k^2*v*c[1]+4*k^2*w*c[1])*(diff(diff(U(xi), xi), xi))+(24*alpha*s*c[1]+v*c[1])*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi)) = 0

 (14)
> 

IM := 24*U(xi)*k^2*s^2-24*U(xi)*k^2*w^2-24*U(xi)*alpha*k^5*s*c[1]+240*(diff(diff(U(xi), xi), xi))*alpha*k^3*s*c[1]-24*U(xi)^3*beta*k*s*c[2]-120*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*alpha*k*s*c[1]+U(xi)*k^5*w*c[1]+4*(diff(diff(U(xi), xi), xi))*k^3*v*c[1]-6*(diff(diff(U(xi), xi), xi))*k^3*w*c[1]+24*U(xi)^3*k*w*c[2]-4*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k*v*c[1]+(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k*w*c[1]-24*(diff(diff(U(xi), xi), xi))*s^2+24*(diff(diff(U(xi), xi), xi))*v^2 = 0
> 

collect(IM, {U(xi), diff(U(xi), xi), diff(U(xi), `$`(xi, 3)), diff(diff(U(xi), xi), xi), diff(diff(diff(diff(U(xi), xi), xi), xi), xi), diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi)})
> 

P := %

(-24*beta*k*s*c[2]+24*k*w*c[2])*U(xi)^3+(-24*alpha*k^5*s*c[1]+k^5*w*c[1]+24*k^2*s^2-24*k^2*w^2)*U(xi)+(240*alpha*k^3*s*c[1]+4*k^3*v*c[1]-6*k^3*w*c[1]-24*s^2+24*v^2)*(diff(diff(U(xi), xi), xi))+(-120*alpha*k*s*c[1]-4*k*v*c[1]+k*w*c[1])*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi)) = 0

 (15)
> 

NULL
> 

NULL
> 

C1 := v = solve(24*beta*s*c[2]+24*v*c[2] = 0, v)

v = -beta*s

 (16)
> 

C2 := w = solve(120*alpha*k^4*s*c[1]+k^4*v*c[1]-4*k^4*w*c[1]-48*k*s^2-48*k*v*w = 0, w)

w = (1/4)*(120*alpha*k^3*s*c[1]+k^3*v*c[1]-48*s^2)/(k^3*c[1]+12*v)

 (17)
> 

C3 := alpha = solve(-240*alpha*k^2*s*c[1]-6*k^2*v*c[1]+4*k^2*w*c[1] = 0, alpha)

alpha = -(1/120)*(3*v-2*w)/s

 (18)
> 

ode1 := subs({C1, C2, C3}, P)

(-24*beta*k*s*c[2]+6*k*(120*alpha*k^3*s*c[1]+k^3*v*c[1]-48*s^2)*c[2]/(k^3*c[1]+12*v))*U(xi)^3+((1/5)*(3*v-2*w)*k^5*c[1]+(1/4)*k^5*(120*alpha*k^3*s*c[1]+k^3*v*c[1]-48*s^2)*c[1]/(k^3*c[1]+12*v)+24*k^2*s^2-(3/2)*k^2*(120*alpha*k^3*s*c[1]+k^3*v*c[1]-48*s^2)^2/(k^3*c[1]+12*v)^2)*U(xi)+(-2*(3*v-2*w)*k^3*c[1]-4*k^3*beta*s*c[1]-(3/2)*k^3*(120*alpha*k^3*s*c[1]+k^3*v*c[1]-48*s^2)*c[1]/(k^3*c[1]+12*v)-24*s^2+24*beta^2*s^2)*(diff(diff(U(xi), xi), xi))+((3*v-2*w)*k*c[1]+4*k*beta*s*c[1]+(1/4)*k*(120*alpha*k^3*s*c[1]+k^3*v*c[1]-48*s^2)*c[1]/(k^3*c[1]+12*v))*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi)) = 0

 (19)

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how do I use dsolve() to solve a ordinary diffe...

Asked by: Dkunb 70
ode dsolve numeric
May 08 2025
1  12

I am not sure how to use dsolve for my problem.
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