MaplePrimes Questions

This ode has solution when solving for the IC by hand. But Maple gives new error I did not see before when asking it to solve the ode with IC. 

No error if asked to solve the ODE without the IC.

Is this new error in dsolve? I have no earlier Maple versions to check. Below is worksheet. Solving for the IC by hand gives the solution which odetest verified.

restart;

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 1789 and is the same as the version installed in this computer, created 2024, August 10, 8:50 hours Pacific Time.`

ode := diff(y(x), x) = sqrt(2)*sqrt(-(y(x) - 6)*(2*y(x) - 3))/(-y(x) + 6);
IC:=y(0)=3;

diff(y(x), x) = 2^(1/2)*(-(y(x)-6)*(2*y(x)-3))^(1/2)/(-y(x)+6)

y(0) = 3

sol:=dsolve(ode);

x-(1/4)*(-4*y(x)^2+30*y(x)-36)^(1/2)-(9/8)*arcsin((4/9)*y(x)-5/3)+c__1 = 0

sol_with_IC:=dsolve([ode,IC]); #why this error??

Error, (in dsolve) when calling 'series/RootOf'. Received: 'unable to compute series'

#lets solve for the IC by hand:
eq:=eval(sol,[y(x)=3,x=0])

-(1/4)*18^(1/2)+(9/8)*arcsin(1/3)+c__1 = 0

C_sol:=PDEtools:-Solve(eq,_C1);

c__1 = (3/4)*2^(1/2)-(9/8)*arcsin(1/3)

my_new_sol:=eval(sol,C_sol)

x-(1/4)*(-4*y(x)^2+30*y(x)-36)^(1/2)-(9/8)*arcsin((4/9)*y(x)-5/3)+(3/4)*2^(1/2)-(9/8)*arcsin(1/3) = 0

odetest(my_new_sol,[ode,IC])

[0, 0]

 


 

Download internal_error_when_unable_to_find_solution_august_22_2024.mw

i have solution of ODE but again i want take derivative from solution function F then i want take reciprocal of derivative
if F'=G then i want 1/F'=1/G like that i want all solution by list and if possible don't give the parameter a sequence  it will be better

thanks for any help

K := diff(G(xi), xi $ 2) = -lambda*diff(G(xi), xi) - mu;
                 2                                    
                d                    / d        \     
          K := ----- G(xi) = -lambda |---- G(xi)| - mu
                   2                 \ dxi      /     
                dxi                                   

V:= [seq](-1..1, 1/2);
                          [    -1     1   ]
                     V := [-1, --, 0, -, 1]
                          [    2      2   ]

interface(rtablesize= nops(V)^3):
DataFrame(
    <seq(seq(<a | b | rhs(dsolve(eval(K, [lambda,mu]=~ [a,b])))>, a= V), b= V)>,
    columns= [lambda, mu, F]
);

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Dear Expert Users,

I am still struggling with my transition from Mathcad 15 to Maple. Would someone be so kind to look at the attached worksheet and how I can obtain the desired result? Thanks in advance. The data used in the example come from TestFleck.xlsx

QuestionPrimes.mw TestFleck.xlsx

Hi
my odetest must give me zero everything is true but still not simplify the function with power include 1/n  not do cancelation even

test_sol_for_PDE.mw

*****************************

EDIT: Thanks for the help i used the restore backup feature. I made my anti virus not react to maple since i thought that might work, so far no more problems. Else this is a fix if anybody else has this problem.

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Hi, so my maple freezes during simple tasks, such as trying to type something, or somtimes copying and inerting the results from a previous equation, the feature where you mark something and drag the answer to somewhere else also does this. When this happens, maple completely freezes and i'm forced to close the app with taksmanager, where i lose everything i have worked on, sometimes for the past hour because i didn't save every minute which is basically not something you can do.

Is there any fix for this or anything i can do to prevent this, cause it really sucks. 

I'm on a windows 11 with maple 2024

i have  written summation with  two  loops at the end and the result should be start from uNew[1][1] since values of i is starting from 1 but in the result i am getting uNew[0][1] why? for understanding of question i am attaching my file kindly help me sort out the problemautomatic_differentiation.mw

Hi
most of my equation when i wanna solve it is give me something like thus equation and it take a lot time to calculate and i don't get any answer after 1 hour past and still searching for finding parameter how i can do in fast way or maybe if exist  can i use mathematica or matlab is better for calculating this or not ?

F-P.mw

I am preparing some examples to start the year in the differential equations lesson. And I was wondering if there is any other way to represent the equilibrium points than the following which I found and then plotted using pointplot.

restart

NULL

alpha := 0.4e-1; beta := 0.8e-2; sys := {diff(g(t), t) = -.25*g(t)+beta*p(t)*g(t), diff(p(t), t) = .7*p(t)*(1-(1/100)*p(t))-alpha*p(t)*g(t)}; ics := {g(0) = 5, p(0) = 20}
 

sol := dsolve(`union`(sys, ics), {g(t), p(t)}, numeric, range = 0 .. 50); with(plots); plots:-display(plots:-odeplot(sol, [t, p(t)], 0 .. 50, color = blue, legend = ["p(t)"]), plots:-odeplot(sol, [t, g(t)], 0 .. 50, color = red, legend = ["gt)"]), labels = ["t", "Population"], title = "Population Dynamics")

 

eqns := {.7*p(t)*(1-(1/100)*p(t))-alpha*p(t)*g(t) = 0, -.25*g(t)+beta*p(t)*g(t) = 0}; eq_points := solve(eqns, {g(t), p(t)}); eq_points

{g(t) = 0., p(t) = 0.}, {g(t) = 0., p(t) = 100.}, {g(t) = 12.03125000, p(t) = 31.25000000}

(1)

eqpoints := pointplot([[0, 0], [100, 0], [31.25000000, 12.03125000]], color = [red], symbol = diamond, symbolsize = 15)

``
phaseplot := odeplot(sol, [p(t), g(t)], 0 .. 35, color = green, thickness = 2)

with(DEtools); vectorfield_plot := dfieldplot([diff(p(t), t) = .7*p(t)*(1-(1/100)*p(t))-alpha*p(t)*g(t), diff(g(t), t) = -.25*g(t)+beta*p(t)*g(t)], [p(t), g(t)], t = 0 .. 35, p = 0 .. 150, g = 0 .. 30, arrows = small, color = blue, axes = boxed)

 

 

display([vectorfield_plot, phaseplot, eqpoints])

 

NULL


 

Download aquarium.mw

Hello,

How can I reduce time calculations for the integral process?

Determining H[1] and HH[1] is very boring!!

 

time_consuming_calculations.mw

Strange thing happening when changing the view zoom factor, as images are not scaling.

That makes it very difficult to generate print documents, a case we've talked about previously.

The first image is a screenshot with 100% scale factor, the other one with scale factor 400%.

One could argue, that I could switch to Print Layout Mode. But the problem there is that I don't have any view zoom factor at all.

I was looking at coulditbe  to see if I can use it to check if odetest result can be zero or not.

But I am finding very strange results. It gives false positive too many times.

Here is an expression in x only. Plotting this it is clear it is never zero for any x value. Also asking Maple to solve this expression=0 for x, it finds no solution.  Yet, when I say coulditbe(e=0) it says true. also is(e=0) returns false.

How could this be possible?  How did coulditbe determine there is some x which makes this expression zero? Is there a way to make sure this function do not give false positive in this example? do I need to add some assumptions may be? 

Should I use is(e=0) instead of coulditbe(e=0) if  the is is more reliable?  have not used these commands much before and was looking for better ways to check if the residual from odetest can be verified it is zero or not.

I also added _EnvTry:='hard'; but it made no difference.  It still gives true.

Maple 2024.1 on windows.

restart;

e:=sqrt(2)*sqrt((3*x^3 + 5*sqrt(x^2 + 8)*x^2 + 24*x + 36*sqrt(x^2 + 8))/sqrt(x^2 + 8))/8 + x/8 + (3*x^2)/(8*sqrt(x^2 + 8)) + 3/sqrt(x^2 + 8);

(1/8)*2^(1/2)*((3*x^3+5*(x^2+8)^(1/2)*x^2+24*x+36*(x^2+8)^(1/2))/(x^2+8)^(1/2))^(1/2)+(1/8)*x+(3/8)*x^2/(x^2+8)^(1/2)+3/(x^2+8)^(1/2)

plot(e,x=-10..10,y=0..4 );

is(e=0);

false

solve(e=0,x); #no solution

x

coulditbe(e=0)

true

_EnvTry:='hard';

hard

coulditbe(e=0)

true

 


 

Download coulditbe_question.mw

Update

I just found out that by adding  assume(x::real); before the call to coulditbe or by adding assuming, then it no longer returns true, but now returns FAIL.

This is much better. At least not a false positive.

So it looks like it was assuming x (and any other parameter than can be in the expression) can be complex and for some complex x, this expression can be zero.

So I will add this assumption now. So I think this will work. But need to test it more.

coulditbe(e=0) assuming x::real;

            FAIL

if I have arational function f(x) in C(x), where C is the complex field, then the partial fraction of f can be written as 

f(x)=p(x)+\sum_{i=0}^n a[i]/(1-b[i]*x)^c[i]
i.e., every denominator is linear in x.

How can I get this factorization in maple, and I think when the degree of the denominator is too high, we can not get the explicit a[i] and b[i], in this situation, can we get their minimal polynomials?

Good morning, I'm trying to evaluate this equation when x = 10 degrees so that it gives me a value something like this -0.1671897 etc. but I can't find a way to do it. I've tried to do it like this:

with(Degrees);
evalf(eq, tand(10));

with(Units:-Simple);
evalf(eq, tan(10*Unit(degree) ;

But it gives me an error. In other words, how do I evaluate the equation at 10 degrees.

 


A few times ago I asked a question about the best way to upload a bunch of files and was told that I had to create a zip file and upload it.

The post I want to create is about the packing of "balls" in "unit boxes" (in arbitrary dimension). I have about 10 Maple worksheets and more than one thousand result files (likely about a hundred of hours of computation).
The size of the zip file is about 260 Mb and the link cannot be inserted (it does not even appear in the list of the uploadable files).

What do you recommend?

TIA

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