@Samir Khan

First, thanks for the release.

But if you could allocate your valuable time and resources to improving the Maple debugger to make it easier to use (as with Matlab's debugger), that would benefit many more people

https://www.mapleprimes.com/posts/209233-Why-No-Improvements-Made-To-Maple-Debugger

@Kitonum 

"Do you understand it? " No. some background: That is why I wanted to use Maple to check. In

F is meant to be what is called first integral, which is constant. Here is from the textbook

So I was trying to see what the computer will give for n=2 system using dsolve to find F(x_1,x_2). I was little surprised by Mathematica result, so wanted to use Maple to check. btw, I tried pdsolve and got same error.

pde:=D[1](F)(x(t),y(t))*diff(x(t),t)+D[2](F)(x(t),y(t))*diff(y(t),t)=0;
pdsolve(pde,F(x(t),y(t)))

(In Mathematica, there is no pdsolve, as dsolve solves both ode's and pde's).

@Kitonum 

I am still getting an error

dsolve(diff(F(x(t),y(t)),t)=0)

Error, (in dsolve) Required a specification of the indeterminate function

dsolve(diff(F(x(t),y(t)),t)=0,F(x(t),y(t)))

Error, (in dsolve) expected the indeterminate function as, say, F(x) where x is of type "name" - and also cannot be a procedure name. Received: [F(x(t), y(t))]

I also do not see difference in result or applying what I had, which is

           D[1](F)(x(t),y(t))*diff(x(t),t)+D[2](F)(x(t),y(t))*diff(y(t),t)=0;

And your (much shorter way of writing the above)

          diff(F(x(t),y(t)),t)=0 

as far how to use it in dsolve to obtain same solution as Mathematica gives?

@Carl Love 

"Is it proper to have a boundary condition with a differential order the same as the highest differential order of the same independent variable as appears in the PDE?"

Correct, It is not proper. That is why I said the PDE is not well posed. Someone wrote this PDE on different forum.

Mathematica does not solve it. I was just wondering what Maple will do with it, that is all. I did not expect to get a solution. It would be better not to give a solution than give wrong one.

Thanks

I do not use 2D at all in Maple. It is horrible.

But  are these multiplication sign there between the "d" and the "T" in  d.T/dt.(t)  (those small dots there in between?)  

If you write Maple using the normal Maple language (i.e. plain 1D text) then one can see the actual code, not try to guess what is hidden behind the 2D letters.

When you write Maple for long code, you have to use plain text editor and have to use Plain text code as normal worksheet are not the right place for large programs in Maple. So the sooner you learn to use normal Maple 1D code the better it is.

@28th 

You are right. You can tell it to use assumptions by using 'useassumptions'=true but then it does not find the positive solution, it returns empty solution. with no assumptions it finds only the negative solution. I do not know why. so I deleted my answer.

@Christopher2222 

thanks for checking. Yes, no issues in 2019 or 2019.1. This problem just started few days ago after upgrading to 2019.2. It also fails in document mode.

@acer 

All what I said  is that using identity, it is possible to simplify the specific example you showed to zero. That is all. I was not saying it will solve any general other relations you might have.

But I deleted it, as it is not needed.  No problem.

@ecterrab 

"I do not see the roadmap" I am trying to find this.

But these 2 posts below does a good job summarizing the stages to go through to graduate from area 51 and become an official stack exchange web site.

Notice that this is just for graduation phase from area 51. After becoming an official stackexchange site, there is no more any such requirments on how many questions per day, and any such thing. The site then just runs on its own.

https://area51.meta.stackexchange.com/questions/28124/minimum-number-of-people-for-a-successful-proposal

https://area51.meta.stackexchange.com/questions/28183/when-can-example-questions-be-answered

Here is the summary from the above:

There are 3 phases to complete: 1. definitions, 2. Commitment 3. beta.  Maple last time went to Commitment phase only and stopped there.

"A proposal needs 60 followers to complete the definition phase."

"200 committers, at least 100 of which have 200+ rep on any other site, and a high enough commitment score"

"Broadly speaking, you will need a community of at least 300-400 avid users (minimum!) "

"The second hurdle is Commitment where you'll need at least 200 users to "commit" to using the site if we create it. 100 of those users will have to earn at least 200 reputation on other Stack Exchange sites to move the proposal on to the Private Beta."

"Finally, if the proposal makes it to Private Beta, you will have about three weeks to attract enough users to curate at least 150 high-quality questions to become a fully listed public site"

So the bottom line, is having lots of users ready to sign up for it. At least 400 or so users (but with half with high reps, 200+) is all what is needed. From the screen shot above by Acer, there was 120 users commited on last attempt.  (I do not know if there was more after that screen shot was taken). I also rememebr many did not have high reps (i.e. over 200 rep) so those users did not count, and that was one of the main reason why Maple did not make it.

There is also a time limit to obtain this number. I do not know know the time. May be few months or so. Will try to find out.

@ecterrab 

If I remember right, there was a first proposal about 7-8 years ago (any one else remembers?). And then another one about 2 years ago. I forgot now the person who initiated it.  Both were closed.

https://area51.stackexchange.com/proposals/70511/maple 

https://www.mapleprimes.com/posts/207987-StackExchange-Site-For-Maple

They remove the actual proposal web pages once it is closed (too bad) so one can't go visit these in order to use the same good questions posted there and same defintions to avoid having to do all of this again and to see the activitiy that happened. But someone with over 10,000 reputation in Area 51 can still see them. I do not have this high reputation myself in area 51.

I remember having a screen shot of it at one point but can't find it.

To get an idea what is needed for proporsal to successed, here is Mathematica's one from about 7 years ago.

https://area51.stackexchange.com/proposals/37304/mathematica

From https://area51.stackexchange.com/faq

I do not know if a deleted proposal can be "reopened". I think one needs to start one from scratch all over again. I'll try to find out. May be someone here knows.

But before doing any of this, we need to make sure there will be enough interest and more users this time to make it pass. Otherwise the same thing will happen like the last two times.

of course having a Maple stack exchange site will surely benefit Maple greatly.

For one thing, searches will be easier, one can enter Latex directly in the question/answer, finding answers and questions will be easier, there will be a chat room; (Which can really be good for building a community) and commenting will be easier, and the forum is much faster and easier to use and has many more features. 

There is a Maple tag at stack overflow [moderator: stackoverflow, math.stackexchange], but it is hardly used and it is not the same as having own site at stackexchange really, like Mathematica.

But this has been tried before two times allready, and both times it failed to gather enough interest to pass the threshold needed in area 51. It is not clear why that is. (myself voted for it in both cases).  So I am afraid trying a third time, will not give a different result.

@Mariusz Iwaniuk 

I am not familiar with this notation %, what is the difference between 

            f1 := (t, w) -> %invlaplace(1/(s^2*w^2), s, t)

and

            f1 := (t, w) -> invlaplace(1/(s^2*w^2), s, t)

And when should one use %?

ps. I use only worksheet mode.  When I used the second form above, I get OK result for some of the results you show. For example

@ecterrab 

Thank you very much for the quick fix.  

I wonder why Maple does not determine the eigenvalues and eigenfunction with periodic boundary conditions when the IC is missing? The solution given is correct, but not the most general one. What I mean, if Maple found the eigenvalues and eigenfunctions, then the solution should be

But Maple gives

Only when adding IC, does Maple  find the eigenvalues and eigenfunctions

But finding the eigenvalues and eigenfunctions does not depend on the IC being there and can be found separately and independent of what the IC is since those come from the spatial boundary value ODE.

This seems to happen only when the BC are periodic. For non-periodic BC, Maple does find eigenvalues and eigenfunctions OK. Here is an example

pde:=diff(u(x,t),t)=diff(u(x,t),x$2); 
bc:=u(0,t)=1,u(Pi,t)=0;
maple_sol:=pdsolve([pde,bc],u(x,t))

Hopefully in future versions Maple can do the same when BC are periodic.

Please find my hand solution in PDF file attached below for this problem.

Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/pde_sol.mw .
 

Download pde_sol.mw

sol.pdf

(Unable to insert content of worksheet for some reason)

@ecterrab 

thank you for the additional information about implicit solution. 

I never said the software is random. I only reflect what I see as a user, since I do not know the internals.

It also works with implicit solutions. I mean changing _C1 to C[1] on an implicit solution gives 0. 

ode:=x*diff(y(x),x) = y(x)-x*(x-y(x))*sqrt(x^2+y(x)^2);
sol:=dsolve(ode,y(x),'implicit');
odetest(sol,ode);
new_sol:=subs(_C1=C[1],sol);
odetest(new_sol,ode);

Both calls to odetest give zero above

Here is another example

ode:=x*diff(y(x),x) = y(x)+a*sqrt(y(x)^2+b^2*x^2);
sol:=dsolve(ode,y(x),'implicit');
odetest(sol,ode);
new_sol:=subs(_C1=C[1],sol);
odetest(new_sol,ode);

Both calls to odetest give zero above

fyi, I run both above in Maple 2018 since my Maple 2019 is busy now running a long running program which takes hrs to complete.

But thank you again for the explanation. I am all set now, as I change C[1] to _C1 just in case before using odetest.

@acer 

thanks. Will try to integrate your code above in my program and see if it works. I have 10's of thousands of Maple expressions that I convert to Latex. This issue with `1` is very minor compared to the many other problems with the latex that Maple generates.