Maple Questions and Posts

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Bernoulli first order ode has form as show in wikipedia  and also on Maple own site as

Notice that it is P(x)*y above and not P(x)* y^(-1) so the y(x) must be linear in that term.   But when I give Maple this ode

ode:=diff(y(x),x) + x*y(x)^(-1)= y(x)^(-1);

Which is clearly not of the form above, it solves it as Bernoulli.  In the above ode, P(x) is x and Q(x) is 1 and n is -1.

The ode advisor correctly said it is separable. But trace shows it used Bernoulli. Also when asking it to solve it as Bernoulli, it does.

What Am I missing here?  Is it not wrong for Maple to use Bernoulli method on this ode which is not Bernoulli?

Worksheet below

interface(version);

`Standard Worksheet Interface, Maple 2024.1, Windows 10, June 25 2024 Build ID 1835466`

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1805 and is the same as the version installed in this computer, created 2024, September 3, 11:35 hours Pacific Time.`

libname;

"C:\Users\Owner\maple\toolbox\2024\Physics Updates\lib", "C:\Program Files\Maple 2024\lib"

restart;

ode:=diff(y(x),x) + x*y(x)^(-1)= y(x)^(-1);
IC:=y(1) = 0;
DEtools:-odeadvisor(ode);

diff(y(x), x)+x/y(x) = 1/y(x)

y(1) = 0

[_separable]

infolevel[dsolve]:=5;

5

dsolve(ode,y(x));  #why this says it solved it as Bernoulli ?

Methods for first order ODEs:

--- Trying classification methods ---

trying a quadrature

trying 1st order linear

trying Bernoulli

<- Bernoulli successful

y(x) = (-x^2+c__1+2*x)^(1/2), y(x) = -(-x^2+c__1+2*x)^(1/2)

dsolve(ode,y(x),[Bernoulli])

Classification methods on request

Methods to be used are: [Bernoulli]

----------------------------

* Tackling ODE using method: Bernoulli

--- Trying classification methods ---

trying Bernoulli

<- Bernoulli successful

y(x) = (-x^2+c__1+2*x)^(1/2), y(x) = -(-x^2+c__1+2*x)^(1/2)

 

 

Download why_this_ode_bernullli_sept_15_2024.mw

Dear Maple community,

I was going to export my math assignment about vector functions as an PDF, when I noticed that it butchered every column vector printed out in blue in the document as math-output. I only have this issue when exporting my work.

How do I make Maple display both coordinates of vector in the blue output field?

I produced the below image as an illustration of my problem:

Thank you in advance.

I am now running eveything in cmaple.exe for number of reasons. But I find the plot generated do not show grid lines as it does in worksheet (GUI). 

Below is worksheet I used, and below that the .mpl file used for command line with the command used.
 

interface(version);

`Standard Worksheet Interface, Maple 2024.1, Windows 10, June 25 2024 Build ID 1835466`

restart;

plot(x, x=0..1, axis=[gridlines=[10, color=blue]]);

 


 

Download why_no_grid_in_cmaple_sept_15_2024.mw

Here is the T.mpl file

currentdir("C:/tmp");  #change as needed

#the following commnad below export a plot to a file

plotsetup(ps, plotoutput="t.ps",plotoptions=`color,noborder`);

p0:=plot(x, x=0..1, axis=[gridlines=[10, color=blue]]):

print(p0); #this will create t.ps in same folder

plotsetup(default); #rest back to default

quit;

 

Now I run the above as follows

"C:\Program Files\Maple 2024\bin.X86_64_WINDOWS\cmaple.exe"   T.mpl

Next I convert t.ps to t.pdf using Adobt PDF pro. The output is this

You see, there are no grid lines. I tried changing the color to BLUE, but it made no difference. Tried difference colors also. nothing worked.

Is there a way to keep the grid lines when using cmaple.exe?

I also attached  t.pdf converted by adobe from the .ps file. Mapleprime will not let me attached t.ps file.

t.pdf

 

 

Is this new error in Maple? I do not have older versions to check.

Solved this ode as series. When calling odetest on it, it gives this error as shown in worksheet below.

Maple 2024.1.

Any work arounds?
 

interface(version);

`Standard Worksheet Interface, Maple 2024.1, Windows 10, June 25 2024 Build ID 1835466`

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1805 and is the same as the version installed in this computer, created 2024, September 3, 11:35 hours Pacific Time.`

libname;

"C:\Users\Owner\maple\toolbox\2024\Physics Updates\lib", "C:\Program Files\Maple 2024\lib"

restart;

ode:=-(A/( (1-x)*x^4) - B/( x^4*(1-x)^2)+C/( (1-x)*x^2))*y(x)+1/(1-x)*diff(y(x),x)+diff(y(x),x$2)=0;

-(A/((1-x)*x^4)-B/(x^4*(1-x)^2)+C/((1-x)*x^2))*y(x)+(diff(y(x), x))/(1-x)+diff(diff(y(x), x), x) = 0

Order:=3;
maple_sol:=dsolve(ode,y(x),'series','point'=1);

3

y(x) = c__1*(x-1)^(1-(1-B)^(1/2))*(series(1-((-4*B+A+C)/((1-(1-B)^(1/2))^2+B-1))*(x-1)+((4*A*(1-(1-B)^(1/2))^2-10*B*(1-(1-B)^(1/2))^2+2*C*(1-(1-B)^(1/2))^2+A^2-4*B*A+2*A*C+6*B^2-6*B*C+C^2-4*A+10*B-2*C)/(((1-(1-B)^(1/2))^2+B-1)*((1-(1-B)^(1/2))^2+B+2-2*(1-B)^(1/2))))*(x-1)^2+O((x-1)^3),x = 1,3))+c__2*(x-1)^(1+(1-B)^(1/2))*(series(1-((-4*B+A+C)/((1+(1-B)^(1/2))^2+B-1))*(x-1)+((4*A*(1+(1-B)^(1/2))^2-10*B*(1+(1-B)^(1/2))^2+2*C*(1+(1-B)^(1/2))^2+A^2-4*B*A+2*A*C+6*B^2-6*B*C+C^2-4*A+10*B-2*C)/(((1+(1-B)^(1/2))^2+B-1)*((1+(1-B)^(1/2))^2+B+2+2*(1-B)^(1/2))))*(x-1)^2+O((x-1)^3),x = 1,3))

odetest(maple_sol,ode,'series','point'=1)

Error, (in odetest/series) when calling 'MultiSeries:-multiseries'. Received: 'unable to sort exponents, {(1-B)^(1/2), -(1-B)^(1/2), 1-(1-B)^(1/2), 1+(1-B)^(1/2), 2-(1-B)^(1/2), 2+(1-B)^(1/2), 3-(1-B)^(1/2), 3+(1-B)^(1/2), 4-(1-B)^(1/2), 4+(1-B)^(1/2)}, MultiSeries:-multiseries'

 


 

Download error_odetest_series_sept_14_2024.mw

I don't know how make my graph be beter for real part and imaginary part and abs part which part how work with parameter can any one explain on this example?

G.mw

i did two case of this equation and odetest is worked good but in this case the odetest is not worked well anyone can determine what is mistake ?

F_P_Correct_case_three.mw

Dear Maple user I am facing error while running the codes  to plot the graph for two data sets .

I am attaching the files.

Error_in_Display_1.mw

HTR.mw

In above problem, Additionally How to  plot  heat transfer rate  Q versus L^2  for distinct porosity parmeters(Sh) , using  heat transfer rate formula, Q = (q*L)/(k*A*T[b])=theta'(1).

using  [Sh = 0.1, L^2 = 0.1, Nr =0 .1, Ha =0 .1, Pe = 0.1],  [Sh = 0.3, L^2 = 0.3, Nr = 0.1, Ha = 0.1, Pe =0 .1],   [Sh = 0.5, L^2 =0 .5, Nr =0 .1, Ha = 0.1, Pe =0 .1].

I have number of worksheets open. I set each to use its own engine.

If I have one worksheet running a long loop that takes hrs to complete, or even if I have cmaple.exe running long script in command line, and then at same time I open new worksheet and type

             Physics:-Version(latest)

Then I always get this error

This is described here

It seems because Maple was busy running another worksheet. I never see this error if I am not running any other thing in Maple at the time. ( I actually try not to update Physics while running something else in Maple, but sometimes I do not notice that I have something else running).

When I wait for my other worksheet to finish, then close all of Maple and reopen Maple, I see the latest version is installed, at least this is what Physics:-Version() now says.

My question is:  Is it safe to do Physics:-Version(latest) even when Maple is busy running  computation in other separate worksheet or even running cmaple.exe from windows command line? Is there any concurrency/locking issue on the Physics library being updated while it is being open by another worksheet or another server.exe running in background?

All this is on windows 10 pro.

I get my on results but the results are not the same please help me if i did any mistake in my code

 

symmetry_PDESYS_3_time_fraction[1].mw

Hello everyone 

Any one can help to plot a figure as follows 

" A cross section of three colored basins of attraction on an (x, y)

plane at z = 0 and w = 0 for a = 2.48 and b = 0.5. Basins in green, red, and cyan leads to a strange attractor, a limit cycle, and a line equilibrium, 

respectively. The yellow leads to unbounded orbits. " Where the system 

xdot=y 

ydot=z

zdot=w

wdot=-az-bw-y-xy. 

and range of x=[-6,6] and y=[-3,6]. 

Hi everyone, is there any source of Maple competitions? Or related questions? I have a hard time finding books on this subject. I am very interested in Maple and hope to improve my Maple programming skills. In addition to frequently browsing this website, I encounter problems on the Internet sporadically, so I think starting with competition questions will be a quick way to improve.

can someone help me curve fitting these parameeters...i only got 1 for all of this 90As4.mw

restart

with(Statistics)with(plots)with(Optimization)with(LinearAlgebra)

E[1] := 126*10^9E[2] := 11*10^9G[12] := 6.6*10^9G_0__12 := 10.1*10^9nu[12] := .28E_0__2 := 15.5*10^9

true_strain := [0, .406915, .710106, .989362, 1.28457, 1.53989, 1.86702, 2.21011, 2.625, 2.99202]; true_stress := [0, 46.0227*10^6, 81.8182*10^6, 109.091*10^6, 138.068*10^6, 163.636*10^6, 194.318*10^6, 219.886*10^6, 248.864*10^6, 267.614*10^6]; epsilon_dot := 10^(-4)

sigma_t := map(proc (epsilon) options operator, arrow; E[instantaneous]*(1-lambda[90*deg]*epsilon*(sum(P[i], i = 1 .. 10)-(sum(P[i]*exp(lambda[i]*epsilon/epsilon_dot), i = 1 .. 10)))/epsilon_dot)*epsilon end proc, true_strain)

``

obj := sum((sigma_t[i]-true_stress[i])^2, i = 1 .. 10)

indets(obj, name)

{E[instantaneous], P[1], P[2], P[3], P[4], P[5], P[6], P[7], P[8], P[9], P[10], lambda[1], lambda[2], lambda[3], lambda[4], lambda[5], lambda[6], lambda[7], lambda[8], lambda[9], lambda[10], lambda[90*deg]}

(1)

Optimization[Interactive](obj)

The solution was obtained with the following warning:
  no iterations performed as initial point satisfies first-order conditions

 

[Float(infinity), [E[instantaneous] = HFloat(1.0), P[1] = HFloat(1.0), P[2] = HFloat(1.0), P[3] = HFloat(1.0), P[4] = HFloat(1.0), P[5] = HFloat(1.0), P[6] = HFloat(1.0), P[7] = HFloat(1.0), P[8] = HFloat(1.0), P[9] = HFloat(1.0), P[10] = HFloat(1.0), lambda[1] = HFloat(1.0), lambda[2] = HFloat(1.0), lambda[3] = HFloat(1.0), lambda[4] = HFloat(1.0), lambda[5] = HFloat(1.0), lambda[6] = HFloat(1.0), lambda[7] = HFloat(1.0), lambda[8] = HFloat(1.0), lambda[9] = HFloat(1.0), lambda[10] = HFloat(1.0), lambda[90*deg] = HFloat(1.0)]]

(2)
 

NULL

Download 90As4.mw

I apologize for putting the equations in image format, but I thought that this way the community could better understand how to interpret the equations.

Below are 6 letters whose solution must be developed step by step so that the periodic extension of each one can then be done. I can solve all the letters by hand (solving in the notebook), but my big question is, how can I do the commands in Maple step by step so that I can solve them as if I were doing them by hand (look like in my notebool)? I need to check step by step. I would be extremely grateful for the help of any of you.

second part

What is the name of the procedure that provides the information about which steps Maple is using to solve an equation? 

I ask because I think pdsolve is caught in a loop, but I can't see what it is trying.

(I can't think of this name at the moment. And Google Gemini returns nonsense. So, I am hoping that by answering this question, Google Gemini will be "trained.") 

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