Unfortunately, the order of output for commands like solve can change. Sometimes repeated execution of the command will cause the change in order, sometimes it takes a new version of Maple to cause the order to change. So, unless the calculation is interactive and to be used just onece, picking out a member of a sequence of solutions by position in the sequence is not necessarily the best way. Selection based on a property of that member is the safest way, even if it is a bit more difficult.

My experience in maintaining the Advanced Engineering Math ebook is what prompts this note. One of the worst offenders against canonical ordering is the dsolve command, but over the years, more and more cases of fickleness in the solve command have had to be corrected with the addition of special code to make the choice of solution unique.

RJL Maplesoft

@UndergradMaths 

Check the recorded demos available on the following page.

http://www.maplesoft.com/teachingconcepts/

There are more recorded demos here:

http://www.maplesoft.com/webinars/recorded/index.aspx

First, the question asks about rotating about the line "theta-pi/2" but apparently, the minus sign should be taken as an equal sign. At least, that is what was done in the several answers already given.

More important: A volume of revolution is created by rotating a region about an axis that does not intersect the region. If the region is the area bounded by the given cardioid, then the problem is what does it mean to create a solid by rotating the region about an axis that passes through the region? In other words, meaning must be given to the doubling over of such a region on itself when it is rotated. Is the volume to be counted twice? If not, provision has to be taken in the integration to ensure that this doubling of volume is not computed.

RJL Maplesoft

Maple and the Putnam Competition

Philippe Dumas and Bruno Salvy

page 63, MapleTech, Volume 2, Number 2, 1995

All 12 problems of the 1993 competition were examined with the conclusion that six fell to the axe of Maple, five did not appear to yield to a computer algebra system, and one could profitably be explored with Maple.

Unfortunately, this Birkhauser publication no longer exists. Perhaps copies can be found on the shelf of an early Maple enthusiast who hasn't yet retired.

RJL Maplesoft

@Jazen1 

Let's make sure you can at least insert a Task Template into your worksheet.

From the Tools menu, select Tasks, then Browse. This brings up the Table of Contents for the task templates. Find the one you want. Then click one of the two Insert buttons at the top. Insert default content means you insert all the verbiage that goes along with the template. Insert Minimal Content means you get enough to make the template work.

The templates in the Table of Contents don't work. They have to be installed into the worksheet to function.

If you are having problems inserting the task template into the worksheet, then something is really wrong. Let us know - this is important.

RJL

@Jazen1 

Yes, you are experiencing a bug that has finally been removed for the next release of Maple. Meanwhile, you can get the blue border to go away by clicking in the box "adroitly." There are places inside the box where the click "takes" and the border goes away. It drives me nuts also, but the task template does work, eventually.

Alternatively, if you watch the whole video, there's a solution from first principles given for drawing tangent and normal lines. This solution uses the syntax-free paradigm, so it can be implemented through the palettes and the Context Menu.

RJL

For any integer n, the nth-degree Taylor polynomial for exp(x) has n zeros. Yet, exp(x) has neither real nor complex zeros. With this behavior of the limit of a sequence of polynomial approximations in mind, the request to find the zeros of a polynomial of infinite degree strikes me as problematic, and really calls for some precise definitions.

RJL Maplesoft

@Markiyan Hirnyk 

Markiyan, thanks for your care in reading my response. You are again correct - when x=3, the edge of the triangle is being searched and the "max" is at a vertex. I failed to note the three coordinates of the point I located. Had I done so, I'd have seen the error you so quickly spotted. Thanks again.

@Markiyan Hirnyk 

Markiyan is completely correct in pointing out that the "maximum" does not exist.

But to conclude that the maximum does not exist on the given set, one has to go through my calculations first.

@Alejandro Jakubi 

The old Classic interface might have been useful for those whose use of Maple centered on coding. It was not useful for creating expository mathematical documents. My Advanced Engineering Math book was written with great pains in Maple 4. It was a terrible interface for writing some 273 worksheets that comprised that text. The Standard GUI provides a much more robust set of tools for writing such documents.

Apparently, you are claiming that the Standard WORKSHEET with 1D input is not sufficient for programmers. I can't address that issue because I rarely write extensive Maple code. But if that is the case, I doubt that Maplesoft is being malicious in not providing a better environment for coders. As I understand it, it's a matter of resources.

The Maple interface now called "Classic" dates back to the mid 1990s, and was written in software provided by a company that went out of business long ago. It is impossible to provide any new features in this old interface.

The new (Standard) interface that arrived with Maple 10 comes in two flavors. One can open a "Document" or a "Worksheet." The Worksheet resembles the look and feel of the Classic interface, but provides some additional features that were missing from the interface that supported Maple 4-9.5.

Unfortunately for some, the default input mode in either the Document or the Worksheet is typeset math (called by Maplesoft "2D" math). This can be changed in the Tools/Options/Display dialog, where the choice "Maple Notation" in the Input display box reverts input to the linear "text form" Maplesoft calls "1D" and which was the only input mode available in the old Classic interface.

Coding in a Document using 2D math does indeed pose challenges as described in the accompanying article. I believe coding in a worksheet using 1D math would have been more appropriate for the task described herein.

RJL Maplesoft

@as5987 

If you are entering the Do command outside of an embedded component, then you must either load the DocumentTools package via the command with(DocumentTools) or use the long form for each call to Do via the syntax DocumentTools:-Do(.....

@as5987 

After forming the two equations, apply the solve command as you did in the original post. Your problem was not with the solve command, it was with forming the equations by reading values from the Math Containers.

@as5987 

To read the contents of MathContainer0,  you can use the Do command from the DocumentTools package. To read and assign to a variable, say u, use Do(u = %MathContainer0). If the DocumentTools package is not loaded, then use the long form: DocumentTools:-Do.

It looks like your example reads two coefficients, one from MathContainer0 and one from MathContainer1. The equations so generated would then be

x*Do(%MathContainer0) = -y*Do(%MathContainer1), etc. (It looks like there is no implicit multiplication (space) or explicit multiplication between your variables and what you hoped would be read from the math containers.)

@ANANDMUNAGALA 

If dsolve returns an exact solution of an ODE, it would be possible to graph it with the plot command.

It must be that you are obtaining numeric solutions, which require different tools. Here is what I would suggest you investigate.

Q:=dsolve({ODE, ICs}, unknown, numeric):
plots:-odeplot(Q);

Look at the help page for the odeplot command for all the variants that allow you to draw various graphs with the numeric solution dsolve/numeric has generated.

By the way, we are all trying to "guess the question" because we are stumped by your reference to "ode architect solver."