I was recently cleaning up a worksheet to make things more succinct.  In that process I modified how I expressed the series coefficients, Ck.  What seemed to be an innocous change apparently upset MAPLE to the point it cannot process my results.  In the abbreviated worksheet link below I process the results in the previous manner, Ck1, as opposed to my current modification, Ck2.

In the previous manner the results are generated under 3 minutes.  After modifying the expression for Ck, MAPLE cannot seem to process the results at all.  As far as I can tell the Ck1 & Ck2 concur.  So I am perplexed.  Can anyone see what is wrong?  The only thing I can think of is that sin(2*pi*k/T*x) in the denominator might cause the problem.  However, the sin term is cancelled out by the same sin term in S4.

Ck_modification.mw

Hello everyone,

  How do I go around this PDE. I think I have input all the necessary required but its given the error code "Error, invalid input: subs received [beta = .5, v = .5, v__l = 1.0, eta = 1.5, false], which is not valid for its 1st argument". 

Below is attached the code.

pde.mw

Please, anyone with any information should help. Thanking you in anticipation.

how i can pdsolve this equation

Doc186.pdf

I am working with the following differential equation:

$\frac{d^2z}{dx^2}+z=\frac{\cos 2x}{1+\epsilon z},\:\:\:z(-\pi/4)=z(\pi/4)=0$

where modulus of $\epsilon$ is much less than $1$.  The task is then to use perturbation theory (with Maple, if necessary) to show that the second-order approximation to the solution to this DE is:

$z=-\frac{1}{3}\cos 2x +\epsilon\bigg(\frac{1}{6}-\frac{8\sqrt{2}}{45}\cos x - \frac{1}{90}\cos 4x \bigg) + \epsilon^2 \bigg(\frac{2\sqrt{2}x}{45}\sin x - \frac{\sqrt{2}}{90}(\pi + 1)\cos x + \frac{7}{720} \cos 2x - \frac{\sqrt{2}}{90}\cos 3x - \frac{1}{1050}\cos 6x \bigg).$

I will then likely have to use Maple to determine the third-order term $\delta^{3}z_{3}(x)$ and evaluate $z_{3}(x)$ at $x=0$ and $x-\pi/8$.

My starting point is to use the theory for a regular perturbation (since the modulus of $\epsilon$ is much less than $1$).  For the unperturbed equation, I could set $\epsilon=0$ as that would give a simple differential equation which should be solvable.  I can then see that $1/{1+\epsilon z}$ can be expanded to second-order in $\epsilon$ as $1 - \epsilon z + \epsilon^2 z^2 + O(\epsilon^3), which looks promising.  Could someone advise how I put this together?  Do I then have to multiply the unperturbed solution by the expansion in $\epsilon$? 

Dear Users!

Hoped everyone is good. I am facing problem to write the following sigma notation for any m.

Please help me to fix this problem. Thanks

Probably a stupid question, but is there a free version of Maple for students or is this something we have to purchase?  

These are some basic questions on using packages from Maple Cloud. I only used it once or twice so far.

When I click on the "cloud" icon, on top right corner of the menu, I see on the left panel "Math apps" then below it "packages" and then below it is says "installed".

When I click on "installed", I see one package that I installed sometime ago.

1) How does one uninstall a package listed in the "installed" list? I see no option to do this.

2) How does one know if the "installed" package needs to be updated or not? And if so, how does one updated it? 

3) In the "packages" list, I see "physics Updates".  Now,  I did install this earlier (1-2 weeks ago). Then why is it not listed also under the "installed" list? And how does one know if they have installed a package that shows in the "packages" list?

There is no marker or anything there to tell one they have installed it or not.  Is one supposed to go look in the "installed" list to manually check if they installed it or not?

4)What happens if one install a package/app they have installed before. Will the new package overwrite the older version automatically?

5) It seems packages installed go to some temporary folder. Is there a way to configure it, so that all packages installed go to some other user defined folder. This way, if one moves to a new PC or such, they do not lose all the packages they have installed? 

It seems these basic functionalities are missing: 1. option to uninstall a package. 2. Marker of some kind to tell one if they installed something listed in the "packages" list. 3. Marker to tell one if a package they have installed needs to be updated if there is a newer version on the cloud.

Only options I see are: Install, view, share link and search. That is all. All the above also applies to "Math apps".

Using Maple 2018 on windows.

Dear all

Starting from

259^2+1=34*1973

How can we perform  a one round of the Fermat Descent procedure and justify that we can write 1973 as sum of two squares.

Thanks

0^0 gives error ,0^0 is undefined, why  maple gives this result?

The uploaded worksheet animates a cam formed of two Archimedean spirals as the cam rotates, creating vertical motion in a circular cam follower.

DirectSearch is used to locate the centre of the follower, however I experience two problems with this use.

First: DirectSearch places the follower centre sometimes above and sometimes below the cam surface, seemingly at random.

Second: seemingly at random, DirectSearch produces completely wrong values for the follower centre unless its SolveEquations command is executed with the initialpoint values stated in the worksheet. I arrived at these by extensive trial and error.

Why does the first problem occur and is there a way to code SolveEquations to avoid it?

Is there a writeup anywhere which can guide me to correct initialpoint values for a particular SolveEquations attempt?

Archimedian_spiral_cam_follower.mw

Hi Mapleprimes,

I have tried to search solutions online without luck. My problem is this. Suppose I have three equations:

f(x,y,z)

g(x,y,z)

h(x,y,z)

I would solve using solve({f,g,h},{x,y,z}) which would give me solutions x*, y* and z*. I need to assign the solutions to use them in subsequent computations. I would like to impose non-negativity constraints, however. Hence, the solution of x is max(x*,0). Obviously if a non-negativity constraint binds, this affects the solutions of y* and z*. I would like to assign the solutions taking this into account. How would you propose I do this? Bear in mind that the solution of x* might be a-b where the relative magnitudes of paramenters a and b are not given. Further down in my code, I would like to assign values to parameters and then let Maple give me the solutions with the non-negativity constraints. I hope I am making sense.

Thanks very much in advance.

Best,

Christian

Say I have an expression

ex:=sqrt(x)/2h

what do I tell maple to pull the 2h into the sqrt

sqrt(x/4h^2)

Hello everybody,

I'm a newbie in Maple, but as far as I read so far this does not seem to be a trivial question.

I have a very large symbolic expression in Maple, where several terms in the form

appear, with  i = 1, ... , 5 and j = 1, ..., 5. This means that there will appear , , , ..., . For each possible combination (i,j) of powers, I would like to have a separate variable whose name depends on those powers, e.g., m_ij. 
 

Is there a way to do that in a single-line definition, without explicitly define 25 different variables?

If this is not possible, assuming I define all 25 variables I need in advance, would it be possible  substitute them in my large expression, wherever they occur? E.g., assuming to have the following expressions

I would like to get the following

Thank you in advance for your replies!

Hellow sir how to plot stream lines for different values of alpha =6,7,8,9.

 I am attaching the sample graph and codes.
How to get the output like that only.

Thanks in advaned

eq1:= alpha*diff(f(eta),eta$3)+f(eta)*diff(f(eta),eta$2)-diff(f(eta),eta)^2+1:
eq2:= diff(h(eta),eta$2)+f(eta)*alpha*diff(h(eta),eta)-diff(f(eta),eta)*h(eta):
eq3:= diff(H(eta),eta) = h(eta):
bc:= f(0)=0, D(f)(0)=0, D(f)(6)=1, h(0)=0, D(h)(6)=1, H(0)=0:
A1:= dsolve(
     {eq||(1..3), bc}, 
     numeric, method= bvp[midrich], abserr = 1e-10, output= operator
):

psi:= unapply(eval(x*f(eta)+H(eta), A1), (x,eta)):
plots:-contourplot((psi(x,eta), x= 0..6, eta= 0..6),alpha=6);

I've asked Maple to solve an equation, and the result is difficult to read because it is separating single variables into multiple multiplicative instances of that variable raised to different powers. Is there a way to tell Maple to combine all instances of a variable into one instance raised to the appropriate power?

I've already tried simplify.

For example:

pceq := (2/3)*Pi*G*rho^2*R^2:
pnonreleq := (1/5)*(3*Pi^2)^(2/3)*hbar^2*n^(5/3)/m:
rhocomposition := rho = m/((4/3)*Pi*R^3), n = Z*rho/(A*m_p):
obj := subs(rhocomposition, rhocomposition, pceq = pnonreleq):
req := R = simplify(solve(obj, R)[1]);

The above code produces 

In the first place, I can't see why Maple would show what should be (Z/A)^(5/3) as z^3 / (A * [A*Z^2]^(2/3)), but I'd like to somehow tell it to not break up the variables like this.

Is this possible? Thanks for the help.