Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

I cannot remember that this was an issue in Maple 6/9/11, so it must have changed later on up to 22.

The following limit fails to execute

restart;
1/(r_S^5*(_C2*r_S^4 + _C2*r_S^3 + _C2*r_S^2 + f[3](0)*r_S + f[4](0)));
limit(%, f[4](0) = infinity);

It fails to calculate the limit with result as zero.

Thanks

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

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 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.") 

I find thus equation of course i use a little bit seperation by hand, i have 11 equation but i can't get results of parameters i don't know why my code is a little bit old i think and i don't know there is another technique for finding them or not here is the file of mp, thanks for any help

F_P_Correct.mw

for apear each part  remove (:)

As a newbie in Maple2024, my next step is to try to solve a Diophantine equation. Attempts with isolve failed. It is the famous task B3 from the IMO of 1988:

If for integers x and y the fraction (x^2+y^2)/(1+x*y) is a positive integer, then it is actually a square number.

The solution is well known. But I would like to learn how to use Maple using this example and would like some advice.

Best regards, Alfred_F

So I have this Maple document that I worked on yesterday, and now when I open it it just opens as the start-up screen where I can choose between document and worksheet mode. I can see that the file is much larger (900 kb) than an empty document, so it should definitely have the data still in there, but opening it with a text editor I couldn't manage to fix my issue. Does anyone have any tips? I have a back-up of the file (from the restore backup menu), but most of the content is not there, so it would be very helpful to get this one fixed.

Exercises.mw
Thanks in advance, 
Kristian.

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