@C_R I find the same behaviour as you for Windows 11, same build number. 

My understanding was that you are taking the small k limit under the condition that k[i]/k[j] is O(1). So I set the O(1) constant to b and then discarded beyond squared terms in k. That logic gives the same result for the exp(A34) you give here. Since we are doing the small k[s] limit, I can't see why the k[s]^2 term on the denominator wouldn't be neglected relative to the constant term, even if I could derive that expression.

There must be more to it than presented here.

@emendes You can get 20 solutions by solve(eqjerkAB) and 18 by SolveTools:-PolynomialSystem(eqjerkAB) - I'm not sure why the numbers of sulotions are different; in my experience the solution sets are usually the same. But Maple chooses the order of variables here. You can choose a variable order by putting the variables in a list. For PolynomialSystems this is an elimination list so that in general the last ones will be given in terms of the earlier ones. So you might get alpha[9,3,0]=alpha[2,3,0] but then not alpha[2,3,0] = alpha[9,3,0]. So are those two different solutions for you?

For a given order, PolynimialSystem should give an exhaustive list. Perhaps solve tried some different orders and found more solutions. If you want any order I suppose you could try giving different orders to PolynomialSystem, but there are a lot of possibilities.

@C_R Accrding to here, WSL can "run various Linux distributions, such as Ubuntu, Debian, Kali, and more".

You mean without using the Windows Subsystem for Linux? I haven't used it but I think it gives you the best of both worlds.

@Carl Love Yes, but tile vertically seems to be gone :(

@nm If a window has the focus, then holding down the windows key while you hit the right-arrow key puts the window on the right half of the screen; with left arrow to get on left half of the screen

@Alfred_F I immediately thought of adding "assuming m<>n". But that does not remove the terms for which m=n. So assuming adds information. Your idea of a constraint in this example is really a modification of the sum itself, and the solution is to modify the summation into two pieces that omit the offending terms. In that sense @mmcdara and I gave the correct answer. Maple does not have a way of automating this, and sum itself does not have this capability.

In terms of more general commands, in some cases adding an assuming clause will work, where an answer may be obtainable for some conditions on the parameters. For example, there are cases in my worksheet where adding assuming n::posint worked. This is probably as close as it gets to a real answer to your question.

In general, Maple gives generic solutions, which apply for most cases but not all. Several solvers have the option parametric, which breaks down the various cases (Summation, solve etc). For differential equations there is casesplit.

In some cases the conditions/constraints are passed as arguments to the commands, such as solve({eqn, a>0}) or commands in the Optimization package.

Bottom line is it depends on what you are doing.

@salim-barzani If you have exact instructions that can reproduce this, it might be possible to diagnose it.

@Alfred_F The last line of Carl's code does this, but only for a given value of k. So

combine(sin(3*x)*cos(x)^3)

gives

1/8*sin(6*x)+3/8*sin(4*x)+3/8*sin(2*x)

As usual you can go the other way with expand. But few Maple commands will deal with the general case; diff is an exception. It is this issue that makes your example hard. For example

int(sin(3*x)*cos(x)^3/x, x=0..infinity);

immediately gives 7*Pi/16.

@salim-barzani For indefinite integration there is always an arbitrary constant (which Maple doesn't show). If the antiderivative is F(x), then indefinite untegration gives F(x) + c, or just F(x) in Maple. Definite integration from -infinity to x gives F(x) - F(-infinity) and the assumption is that F(-infinity) = 0 since we haven't accumulated any area yet at the start. Maple has Intat to describe integration at a point - you could use Intat(f(a),a=x) instead of indefinite integration.

The main Maplesoft site has said "site under maintenance" with possibly reduced functionality for about the same period (still true today), so looks like the revamp took Mapleprimes offline. The application center was also down for at least some of it.

@nm @Alfred_F Since odetest gives 0 for y(0)=a, it is probably doing something simple like below, though I didn't check its code.

dsolve.mw (won't display right now)

@Alfred_F Maple agrees with you.

expand(PDEtools:-dchange(y(t)=sqrt(u(t)),-ode/t,[u(t)]));
DEtools:-odeadvisor(%);

@acer Thanks for the vote and tips, especially for the limit. I knew there would be another answer for the labelling issue - I tried a few things with typeset and uneval quotes, before moving on.

I've become sold on the advantages of equations that are expressions implicitly equal to zero (I know @nm holds the opposite view). Then there aren't things to cancel, just things to divide by. Many things don't map across the `=` and I find normal and numer etc convenient in this context. It has the disadvantage that it is less readable, but I can live with that.