Hi everyone, I have a problem in the code solving coupled partial differential equations. I could not find out the solution. Please help me out with this. Find the code in the attachment.

This update fixes the problems inadvertently introduced in Maple 2019.2, namely:

• Maple failed to run the code in the maple.ini/.mapleinit initialization files when loading existing worksheets containing a restart() command
• Installing some packages from the MapleCloud was unsuccessful

For anyone who installed the 2019.2 update, installing 2019.2.1 will fix these problems.

If you are at Maple 2019.1 or earlier, installing this update will bring you straight to Maple 2019.2.1.

This update is available through Tools>Check for Updates in Maple, and is also available from our website on the Maple 2019.2.1 download page.

If you are a MapleSim user, please note that these problems do not affect your use of MapleSim. If you use Maple on its own, and if you use Maple command initialization files and/or you need to install a package from the MapleCloud that does not work, please contact Maplesoft Technical Support for assistance.

We sincerely apologize for the inconvenience and thank you for your patience as we worked through this issue.

I'm new to using Maple and am trying to create the procedure above. My code so far:

with(combinat):
g:=proc(n)
 local x; local setG; local setG2;
    for x from 1 to n do
        setG:={seq(x+1,x=1..n-1)}; setG2:=choose(setG,3); nops(setG2);
    end do;
end proc; 

Although this doesn't seem to work even though

setG:={seq(x+1,x=1..5)}; setG2:=choose(setG,3); nops(setG2);

Any help would be greatly appreciated!! 

What is the correct way to specify region where solution of a PDE is needed? For example, I am trying to verify my hand solution to this HW problem: Solve Poisson PDE in 2D 

The above is the only information given in the textbook. So it is only in the upper half plane. If I type this

interface(showassumed=0);
pde := VectorCalculus:-Laplacian(u(x,y),[x,y])=-1/(1+y);
bc:=u(x,0)=0;
pdsolve([pde,bc],u(x,y)) assuming y>0

Maple gives 

But I get by hand using method of images is

So not exactly the same. I think I made mistake in my solution. But I am also not sure that just saying "assuming y>0" is doing what I think it is supposed to do. For example, suppose we want to solve the same PDE say in the first quadrant. Typing

pdsolve([pde,bc],u(x,y)) assuming y>0,x>0

Gives same solution. But the solution should be different. And typing

pdsolve([pde,bc],u(x,y)) 

Gives same answer as well.

So I think I need another way to tell Maple the region of the solution. i.e. I need to tell Maple to use the Laplacian for the upper half plane only and not the Laplacian in the whole 2D space.

Any suggestions what to do and how to handle such problems?

Thank you

When composing multiple plots, plots:-display's normal behavior is to set the overall plotting region to what is necessary to accommodate the union of the individual plots.  That works correctly most of the time but not in the case shown below.  This may indicate a bug in one of plots:-shadebetween,  plots:-display,  plottools:-extrude.  I have not been able to pinpoint the problem.  Any ideas?

This was done in Maple 2019.

Maple 2017 behaves the same way.  I don't know whether this ever worked properly in earlier Maples.
 

Download bug-in-3D-view.mw

Hello;

What trick if any is needed to obtain zero for this sum in Maple?

sum(sin(Pi*n/2)*sin(n*Pi*(x + 1)/2)*cos(n*Pi*t/2),n=1..infinity)

The above sum, according to Mathematica is zero. I am trying to see if same result can be obtained by Maple in order to verify this result. It is possible ofcourse that Mathematica result is not correct. I am also trying to verify the sum is zero by hand, but no success so far.

Here is Mathematica result

Using Maple 2019.2 on windows 10. 

Thanks

Download q2.mw

Hello,

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): mwquestion2.mw

Hello everybody,

I am new to MaplePrimes, so I am sorry for possible bad formatting.

I am solving some physical problem in cylindrical coordinates, so the EDIT independent variables are r,phi,Z. The equations I obtain contain constants _C from dsolve and constant parameters aplha[i,j], for example

I would like to solve this type of equations for all values of the variables, namely phi in the example above.

If I do not choose the variables for which to solve, I get phi=phi as one of the equations in the solution. If i choose all the variables except phi, i get an the expression for the constants containing the variable phi.

Is there a way to solve these equations automatically or do I have to separate them manually using collect and coeffs?

Or could the solution be the comand Parameters from Physics package?

Thank you in advance for your help.

EDIT: I did not explain the problem properly. I am solving some complicated set of determining equations to obtain integrals of motion. They are rce in the attached file. I substitute some ansatz for the magnetic field and I solve them for 

The first set of equation, called third in the file are solved by HOconds_polar_solved. This is where the  konstants alpha[i,j] appear. I substitute HOconds_polar_solved into the equations rce and try to solve them for the remaining functions.

Because it is an overdetermined system, I get some equations of the type in the original question or (for example)

8*r^5*_C1*((alpha[4, 4] - alpha[5, 5])*cos(2*phi) + sin(2*phi)*alpha[4, 5])=0

Because r and phi are the independent veriables of the system, the solution to the equation above should be 

_C1=0 or (alpha[4,4]=alpha[5,5] and alpha[4,5]=0)

But I get the following.

solve(8*r^5*_C1*((alpha[4, 4] - alpha[5, 5])*cos(2*phi) + sin(2*phi)*alpha[4, 5]));
 {_C1 = 0, phi = phi, r = r, alpha[4, 4] = alpha[4, 4], alpha[4, 5] = alpha[4, 5], alpha[5, 5] = alpha[5,5]}, 
{_C1 = _C1, phi = phi, r = 0, alpha[4, 4] = alpha[4, 4],  alpha[4, 5] = alpha[4, 5], alpha[5, 5] = alpha[5, 5]},
 {_C1 = _C1, phi = phi, r = r, alpha[4, 4] = -tan(2 phi) alpha[4, 5] + alpha[5, 5], alpha[4, 5] = alpha[4, 5], alpha[5, 5] = alpha[5, 5]}

The file (part of the original file, which is very long): question.mw

EDIT 2: I changed the title to contain independent variables, which makes the answer more clear. The second Answer from Carl Love works fine, at least in the presented case.

Hi everyone, I'm having a bit of trouble using the dsolve () command in maple, it keeps coming up with error messages.

My assignment is to find the first order differential equation of T_ovn(t), and then I know that you have to define it and then dsolve the definition.

The problem is, that what am I doing wrong?

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

I want to separate  the derivative and non-derivative (the part other than  derivative) terms from the following (shown in figure) equations by using maple commands or code. Kindly help me. Thanks in advance. 

This may be a bug.  In Maple 2019.0

plot3d(x^2+y^2)

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.

Maple 2019.2.

These two expressions are mathematically equivalent:

But simplify(expr1-expr2) does not give zero where simplify(convert(expr1,trig)-expr2) does.

Is this normal behavior or can be expected sometimes? As a user I would have expected Maple internally to figure all of this itself. Compare to Mathematica:

Is there a different command in Maple that will show mathematical equivalence of two expressions to try other than simplify?

Thanks
 

Download q.mw

How to change default directory for Maple 2019?

I'm only just hearing (haven't experienced) about some serious issues with the 2019.2 updates.  I would recommend waiting for Maplesoft to release an emergency 2019.3 fix update - Maplesoft can NOT leave the last update of 2019 in this state.