@John Fredsted For me, the trickiest part of using frontend is always getting that third argument just right. In this case, that's the [{`+`,`*`,`^`, set}, {}]. I welcome any suggestions for the simplification of this argument.

@Mariusz Iwaniuk These are useful worksheets! You should polish these and repost or put them on the Maple Applications Center.

But I need an explanation where the magic numbers 0.5017, 0.6407, 0.6122, and 0.2645*I come from.

See the Wikipedia article on Grigori Perelman. There seem to me to be two main motivating factors: A belief that mathematical prizes are unfair because they don't recognize the contributions of others, and, essentially, an intense hatred of papparazzi.

@nm I understand the desire for "plain text for input and 2D for output"---that's the only way that I use Maple---but why the classical interface? For one thing, the plots are much better in the standard interface.

I don't remember the details---they've been described here before---but there is a specific technical reason why it became impossible to maintain/update the classical interface.

@Allan Wittkopf , wrote, five years ago:

Sorry that the page is not easy to read - the problem is that there's just so darned much to pack in there, and events needed to evolve significantly over the last several releases, so the page grew and grew, so it's quite difficult to follow.

The exposition on the page may have grown and grown, but the examples have not. There should be at least one example for every option. By a very quick count (where I may have repeated some), I count 52 options described on the page. These options are by no means independent. So there's a myriad of meaningful combinations of the options.

No doubt, a great deal of effort went into developing the events system. That effort has largely gone to waste just because of a lack of examples on the help page. I think that there's only a handful of people in the world who understand it.

@taro No, I still say that you are correct that "% before ',' is missed, surely." Whether or not the page's author intended for a % to be there is irrelevant: it should be there. This trend of using equation label references in help pages is deplorable.

The English past participle missed has multiple meanings. It can mean overlooked or forgotten; it can also mean causes emotional pain due to its absence. By contrast, the present participle missing can only mean absent although it was expected without any emotional connotation (as far as I know).

Vote up. Yes, I've been waiting for years for many, many more examples to be added to that help page. There's about 10 times as many options listed as there are examples shown for. The descriptions aren't very useful to me without examples.

First, two small mistakes:

• ms at the end of Eq1 should be m*s.
• h at the end of Eq2 should be h(eta).

Now you need to solve for the highest-order derivatives, and then dsolve separately over the branches.

solve({Eq1,Eq2,Eq3}, {diff(f(eta),eta$3), diff(h(eta),eta$3), diff(theta(eta),eta$2)});
All:= allvalues(%);

Now, in the dsolve command, replace Eq1, Eq2, Eq3 with either All[1][] or All[2][], it doesn't matter which.

At this point, dsolve will complain about complex values. I don't know how to proceed from this point. Hopefully someone else does. Theoretically, it should be possible to solve a matrix-based system of linear equations even if the coefficients are complex.

You should avoid a potentially time-wasting option such as maxmesh= 10000 unless you're sure that it's necessary. If the option will help, dsolve will let you know that by giving you an explicit error message that tells you to increase maxmesh.

Using a simpler example if it's helpful, please explain how this set has anything to do with groups, bases, linear algebra, or echelon form.

A response to my Answer is expected.

@taro Taro is correct. Vote up. That should be

f:= unapply(%, x, y);

There is no Maple syntax where a comma is used as something other than as a separator, and it's never just empty space that's being separated.

Yeah, those pages should be proofread. I'd guess that the program that generates those web pages treats % as a special character, and whoever typed up the page forgot that.

@tomleslie Vote Up. Thank you for noticing the odd-function thing.  The sign of the argument has something to do with it. Also, I think that there may be some difference between polynomials that the user enters (such as b-a+c) and those that are automatically generated such as those that appear as the arguments to ln and arctan in the Question. I'm just guessing about that last sentence.

@nm The critical thing that makes the difference between your examples is the lexicographic ordering of x0 and the other variable. I have no doubt about that. The exact nature of that difference is harder to classify: I'm not saying that every polynomial will appear in lexicographic order. The sign of the polynomial also has something to do with it, and the sign depends somewhat on the lexicographic order. I expanded my Answer, and I hope that that clarifies the matter somewhat.

@zack94 If you post any Maple-related Question, I'll give you 5 reputation.

@Joe Riel Hmm, I'm aware that the value that my program above returns is roughly proportional to kernelopts(stacklimit). It seemed unlikely to me that that knowledge would help the OP, so I didn't mention it. 

So, now that you've mentioned it, do you know of any aspects of the procedure itself (such as its size) that would change the count?