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Dear maple users,
I am solving an ode problem with an analytical solution.
programming running properly, but my plot not exact with the already existing article plot. 
how to get the exact plot.

Thanking you.


N := 3;





dsolve(diff(f(x), `$`(x, 3)));

f(x) = (1/2)*_C1*x^2+_C2*x+_C3


Rf := 2*(diff(f[m-1](x), x, x, x))-(2*mh*mh)*(diff(f[m-1](x), x))+sum(f[m-1-n](x)*(diff(f[n](x), x)), n = 0 .. m-1)-bet*(sum(sum(2*f[m-1-n](x)*(diff(f[n-t](x), x))*(diff(f[t](x), x, x))+f[m-1-n](x)*f[n-t](x)*(diff(f[t](x), x, x, x))+x*(diff(f[m-1-n](x), x))*(diff(f[n-t](x), x))*(diff(f[t](x), x, x)), t = 0 .. n), n = 0 .. m-1));

2*(diff(diff(diff(f[m-1](x), x), x), x))-2*(diff(f[m-1](x), x))+sum(f[m-1-n](x)*(diff(f[n](x), x)), n = 0 .. m-1)-.2*(sum(sum(2*f[m-1-n](x)*(diff(f[n-t](x), x))*(diff(diff(f[t](x), x), x))+f[m-1-n](x)*f[n-t](x)*(diff(diff(diff(f[t](x), x), x), x))+x*(diff(f[m-1-n](x), x))*(diff(f[n-t](x), x))*(diff(diff(f[t](x), x), x)), t = 0 .. n), n = 0 .. m-1))


dsolve(diff(f[m](x), x, x, x)-CHI[m]*(diff(f[m-1](x), x, x, x)) = h*H*Rf, f[m](x));

f[m](x) = Int(Int(Int(CHI[m]*(diff(diff(diff(f[m-1](x), x), x), x))+2*h*(diff(diff(diff(f[m-1](x), x), x), x))-2*h*(diff(f[m-1](x), x))+h*(sum(f[m-1-n](x)*(diff(f[n](x), x)), n = 0 .. m-1))-(1/5)*h*(sum(sum(2*f[m-1-n](x)*(diff(f[n-t](x), x))*(diff(diff(f[t](x), x), x))+f[m-1-n](x)*f[n-t](x)*(diff(diff(diff(f[t](x), x), x), x))+x*(diff(f[m-1-n](x), x))*(diff(f[n-t](x), x))*(diff(diff(f[t](x), x), x)), t = 0 .. n), n = 0 .. m-1)), x), x)+_C1*x, x)+_C2*x+_C3


f[0](x) := 1-exp(x);



for m to N do CHI[m] := `if`(m > 1, 1, 0); f[m](x) := int(int(int(2*CHI[m]*(diff(f[m-1](x), x, x, x))-(2*h*H*mh*mh)*(diff(f[m-1](x), x))+h*H*(sum(f[m-1-n](x)*(diff(f[n](x), x)), n = 0 .. m-1)), x)-h*H*(sum(sum(2*f[m-1-n](x)*(diff(f[n-t](x), x))*(diff(f[t](x), x, x))+f[m-1-n](x)*f[n-t](x)*(diff(f[t](x), x, x, x))+x*(diff(f[m-1-n](x), x))*(diff(f[n-t](x), x))*(diff(f[t](x), x, x)), t = 0 .. n), n = 0 .. m-1))*bet, x)+_C1*x, x)+_C2*x+_C3; s1 := evalf(subs(x = 0, f[m](x))) = 0; s2 := evalf(subs(x = 0, diff(f[m](x), x))) = 0; s3 := evalf(subs(x = 1, f[m](x))) = 0; s := {s1, s2, s3}; f[m](x) := simplify(subs(solve(s, {_C1, _C2, _C3}), f[m](x))) end do:

f(x) := sum(f[l](x), l = 0 .. N);








Analytical solution approach:





Explore the values of km_digit(n,m) using km_ for all m,0 < or equal to m and less than or equal to 8. 

Look at the output until you can make a conjecture that concerns the pattern obtained.

Hint use km_list(m,6,20) when m is not a multiple of 4 and km_list(m,6,50) when m is a multiple of 4

I am studying the motion of a beam coupled to piezoelectric strips. This continuous system is modelled by two DE:

YI*diff(w(x,t), x$4)-N[0]*cos(2*omega*t)*diff(w(x,t), x$2)+c*diff(w(x,t), t)+`&rho;A`*diff(w(x,t), t$2)+C[em,m]*v(t) = 0;


C[p]*diff(v(t), t)+1/R[l]*v(t) = C[em,e]*(D[1,2](w)(0,t)-D[1,2](w)(ell,t));

where "w(x,t)" stands for the beam's vibration and "v(t)" means the electric voltage, which is constant throught the beam. I would like to numerically solve both DE simultaneosly, but maple will not let me do it. I would like to know why. I am getting the following error:

Error, (in pdsolve/numeric/process_PDEs) number of dependent variables and number of PDE must be the same

I suppose it is because "w(x,t)" depends on "x" and "t", while "v(t)" depends solely on time, but I am not sure. Could someone help me out? Here is my current code:

declare(w(x,t), v(t)):

YI*diff(w(x,t), x$4)-N[0]*cos(2*omega*t)*diff(w(x,t), x$2)+c*diff(w(x,t), t)+`&rho;A`*diff(w(x,t), t$2)+C[em,m]*v(t) = 0;
pde1:= subs([YI = 1e4, N[0] = 5e3, c = 300, omega = 3.2233993, C[em,m] = 1], %):
ibc1:= w(0,t) = 0, D[1,1](w)(0,t) = 0, w(ell,t) = 0, D[1,1](w)(ell,t) = 0, D[2](w)(x,0) = 0, w(x,0) = sin(Pi*x/ell):

C[p]*diff(v(t), t)+1/R[l]*v(t) = C[em,e]*(D[1,2](w)(0,t)-D[1,2](w)(ell,t));
pde2:= subs([C[p] = 10, R[l] = 1000, C[em,e] = 1, ell = 5], %):
ibc2:= v(0) = 0:

pdsolve({pde1, pde2}, {ibc1, ibc2}, numeric);


Hello everyone!

I'm interesting in "zcoloring" funciton in colorscheme option.

I wrote simple programm which compares two results: spectrogram of signal drawn with "colormap" list and spectrogram which was plotted with zcoloring function. I use red, green, blue functions to construct JET-colormap: list and expressions in "zcoloring".

My result:

As I understand, when I use:

colorscheme = ["zcoloring", [z-> Red color function(z), z-> Green color function(z), z-> Blue color function(z)], colorspace = "RGB"]

Maple plots z-value with color RGB color coordinates defined from "zcoloring". For example, if "zcoloring" is

colorscheme = ["zcoloring", [z-> 5*z, z-> 3*z, z-> 2*z], colorspace = "RGB"]

and z value is 10, then 10 value will correspond [50,30,20]-RGB color.

My test program:

Spectrogram of my test signal:



a follow up question.

I am solving some overdetermined system of ODEs in cylindrical coordinates r,phi,Z. I obtain some equations of the following type:

(diff(_F1(phi, Z), phi)*r + diff(diff(s_r(phi, Z), phi), phi))/r = -s_r(phi, Z)/r

As can be seen, the differentiated functions do not depend on r, which is an independent variable. Thus, the correct solution is to separate the equation and have 

_F1(phi,Z)=_F1(Z), s_r(phi,Z)=s_r(Z).

By using dsolve, I always obtain a solution containing r.

A similar problem that does no contain derivatives is solved by solve/identity.

Is there something similar for dsolve?

EDIT: I again put here more info and file. I solve some overdetermined system of differential equations.

[diff(s_r(r, phi, Z), r) = 0, diff(s_r(r, phi, Z), phi) = -diff(s_phi(r, phi, Z), r)*r^2,
diff(s_Z(r, phi, Z), r) = -diff(s_r(r, phi, Z), Z), diff(s_phi(r, phi, Z), phi) = -s_r(r, phi, Z)/r, 
diff(s_Z(r, phi, Z), phi) = -diff(s_phi(r, phi, Z), Z)*r^2, diff(s_Z(r, phi, Z), Z) = 0, 
diff(m(r, phi, Z), r) = s_Z(r, phi, Z)*B_phi(r, phi, Z) - s_phi(r, phi, Z)*B_Z(r, phi, Z),
 diff(m(r, phi, Z), phi) = s_r(r, phi, Z)*B_Z(r, phi, Z) - s_Z(r, phi, Z)*B_r(r, phi, Z),
 diff(m(r, phi, Z), Z) = s_phi(r, phi, Z)*B_r(r, phi, Z) - s_r(r, phi, Z)*B_phi(r, phi, Z), 
s_r(r, phi, Z)*diff(W(r, phi, Z), r) + s_phi(r, phi, Z)*diff(W(r, phi, Z), phi) + 
s_Z(r, phi, Z)*diff(W(r, phi, Z), Z) = 0]

After some time, I arrive at the equation in the original question. So the independance of the other functions on r is the consequence of the other equations.

Here is the file (shortened):

   1 1 1 2 2 3 3  

(  1 3 3 2 2 1 2 )

how to input this permutation into permgroup ?


This is another problem I just found in Maple 2019.2 on windows 10. professional.

I wanted to close Maple, so did  File->Exit 


But Maple did nothing. It did not close.  Also Alt-F4 did not close Maple. I had to click on the little X on top right corner of the open window to close Maple.  

In earlier version this used to work to close Maple.

Do others see this as well?  To reproduce, simply start Maple, and do File->Exit.

Here is a movie also


This may be a bug.  In Maple 2019.0


Now grab the graphing window and drag to adjust it's size.  It doesn't adjust it's size until you let go of the mouse button.

If maple can auto discover derived equations, 

then most variable are unknown name which may or may not be physics variable.

so, how to guess which physics data suitable for these look like meaningless variable?

or these tools only visualize the relationship of existing known equations?

How to solve this DE with IC by using DTM.
D^m u(x,t)=u''(x,t)-u^2 (x,t), where n-1< m < n 

IC: u(x,0)=1+sin(x), and u'(x,0)=0

I have a problem for school that I need help with. 

Solve: by variation of parameters.

x3y’’’ – x2y’’ − 2xy’ + 6y = x2

Use any software, e.g. Maple, as an aid in computing roots of the auxiliary equation and the Wronskian-based determinants W, W1, W2, W3

I was able to hand calculate the roots as [m1 = 3, m2 = 2, m3 = -1]


with(VectorCalculus); Wronskian([x^3, x^2, 1/x], x, 'determinant')

Matrix(%id = 18446744078324919462), -12*x


with(VectorCalculus); Wronskian([0, x^2, 1/x], x, 'determinant')

Matrix(%id = 18446744078349556782), 0


with(VectorCalculus); Wronskian([x^3, 0, 1/x], x, 'determinant')

Matrix(%id = 18446744078266878782), 0


with(VectorCalculus); Wronskian([x^3, x^2, 0], x, 'determinant')

Matrix(%id = 18446744078331625094), 0


m3 := Matrix(3, 3, [0, x^2, 1/x, 0, 2*x, 1/x^2, x^2, 2, 2/x^3])

Matrix(%id = 18446744078385724822)


Determinant(m3, method = multivar)

Determinant(Matrix(%id = 18446744078385724822), method = multivar)``


roots(x^3-x^2-2*x+6, alpha, beta)




solve(x^3-x^2-2*x+6 = 0, x)

-(1/3)*(71+9*58^(1/2))^(1/3)-(7/3)/(71+9*58^(1/2))^(1/3)+1/3, (1/6)*(71+9*58^(1/2))^(1/3)+(7/6)/(71+9*58^(1/2))^(1/3)+1/3+((1/2)*I)*3^(1/2)*(-(1/3)*(71+9*58^(1/2))^(1/3)+(7/3)/(71+9*58^(1/2))^(1/3)), (1/6)*(71+9*58^(1/2))^(1/3)+(7/6)/(71+9*58^(1/2))^(1/3)+1/3-((1/2)*I)*3^(1/2)*(-(1/3)*(71+9*58^(1/2))^(1/3)+(7/3)/(71+9*58^(1/2))^(1/3))


m3 := Matrix(3, 3, [0, x^2, 1/x, 0, 2*x, 1/x^2, 1/x, 2, 2/x^3])

Matrix(%id = 18446744078348970214)


Determinant(m3, method = multivar)

Determinant(Matrix(%id = 18446744078348970214), method = multivar)



m3 := Matrix(3, 3, [0, x^2, 1/x, 0, 2*x, 1/x^2, 1/x, 2, 2/x^3])









I have just upgraded my laptop from Windows 7 to Windows 10.  On starting up Maple 2018,  I receive the attached message on screen.  This is after previously loading the worksheet successfully.   Today,  I am not able to do so.  I need to permanently register my firewall to allow Maple to run; can anyone help?



After upgrading to 2019.2 (on windows 10, 64 bit) using the pull down menu option I noticed the following problem.

I create a new worksheet and run it. Here is an example


for i from 1 to 10 do

(the restart is on seperate cell).

It runs OK first time. I close Maple. Restart Maple again, open the same worksheet. Now once I evaluate the restart; command, the kernel crashes. This happens each time.

Any suggestions what to do?  Only fix I found is to copy the content of the worksheet and create a new worksheet, then it runs. But then the new worksheet fails again when I close Maple and restart again. So this is not a solution.

I also noticed it crashes ONLY when running the restart; command/cell. Other commands work OK. So something to do with initialization. I have not changed anything at all on my end after upgrading to 2019.2 from 2019.1.

Evaluating the next cell first thing when opening the worksheet, then it runs OK and no crash.

This only started to happen after updating to Maple 2019.2. No problem with 2019.1. Clearly this version was not well tested.  How could one revert back to 2019.1 ??


To answer comment below. It also happens in document mode:


I have a .mapleinit file that amongst other things sets libname so my own packages are accessible and can be loaded using with(). Imagine my surprise when I found that a maple program that ran half an hour ago on Maple2019 bombed when it did not find its package. Closer investigation indicates that maybe .mapleinit is only searched for in currentdir()??

The updated Maple is `Maple 2019.2, APPLE UNIVERSAL OSX, Oct 30 2019, Build ID 1430966`

The old one is gone :-(. It was Maple2019.0. I should add that on this system, Maple is installed on an administrator account that is not my user account (luckily I have access to that). I am running macOS 10.14.6 Mojave.

I verified my older Maples still work as before.

Has anyone else seen this behaviour?

Mac Dude.

Edit: I need to be more specific here: When I double-click a worksheet (.mw file) then currentdir() will be set to the directory the .mw file is in. This has been long-standing Maple behaviour. But then currentdir() does not cover the home directory where .mapleinit sits. As a result, a blank sheet finds my .mapleinit whereas my files (that habitually I open with double-click or drag-drop) do no longer run the .mapleinit file.


can anyone help me to calculate the exact  value of the eigenvalues of this matrix:


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