## 6996 Reputation

16 years, 214 days

## Amazingly quick fix!...

Hi Edgardo, that's the quickest ever turnaround of a software fix.  Awsome!

And thanks for pointing out the [exact] option.  I didn't know about it either.

As to the documentation of the parametric option, I went to ?dsolve,details and followed the link parametric solving scheme.  That takes to a page that describes a scheme from Kamke's book.  But the focus there is on first order nonlinear equations.  I could not relate the discussion there to my second order linear equation.  Perhaps I am looking in the wrong place.

PS: I just ran into a related issue.  I will post it as a followup to my original question.

## Excellent!...

@acer That's excellent.  I haden't used the parametric option to dsolve before, so I looked up the documentation.  On the first reading, it's not clear to me what Maple does with that option behind the scenes, but it does the right thing anyway, so I am happy.  Thanks for your answer!

## Check the statement...

If then your expression for T(t) reduces to T(t)=15.  Probably that's not what you meant.  Double-check your statement!

## Try a simple case before going for the h...

@Tamour_Zubair As I wrote before, expressing a nonlinear system through matrices is not very productive.  To see that, consider this simple system of nonlinear ODEs:

 diff(x(t),t) = x(t) + y(t); diff(y(t),t) = x(t) * y(t);

Can you tell me how you would like write that as a system with matrices?  And if you do so, in what way will that be useful to you?

## New version of Bark...

I still see no examples directory but that's alright since from what I have figured out by now, this is not something that will be of very much use to me.

## Problem lies elsewhere...

@tomleslie Your statement is true in principle, however that's not the source of OP's problem. Without the symbolic option to simplify() in his worksheet, his calculations would yield the correct result.

@Joe Riel I was intrigued with that description of Bark so I installed it (along with the prerequisite TextTools).

Bark's help page says "The examples subdirectory of the Bark toolbox contains the Maple source for a few shell commands created with Bark."  I am unable to find the examples subdirectory.  This is all there is:

```[14:13 shadow]~> tree maple
maple
└── toolbox
├── Bark
│   ├── lib
│   │   ├── Bark.help
│   │   └── Bark.maple
│   ├── uninstall_manifest.mtxt
│   └── version.txt
└── TextTools
├── lib
│   ├── TextTools.help
│   └── TextTools.maple
├── uninstall_manifest.mtxt
└── version.txt
```

After reading Bark's help page, and not having the examples subdirectory, I have the following questions:

1. Does one execute the shell script (generated by Bark) from within Maple or directly from the Linux command-line?
2. If the latter, then is the shell script self-contained?  That is, can it be executed without Maple present?
3. If the shell script needs Maple to run, then what is its utility? That is, why would one want to run the shell script instead of the original Maple program?

## tangential force...

@tomleslie When a point mass slides down a frictionless incline of angle alpha relative to the horizontal, its weight mg gets decomposed into a normal force to the incline, mg cos α, and a tangential force, mg sinα. So yes, there is a tangential force, and therefore a tangential acceleration.

## Doesn't make sense......

The isochrone property of the semi-cubical parabola is cited in numerous websites.  It appears that it originated in the Mac Tutor website, and other websites just copied that information without verifying it.  Here is what Mac Tutor says:

In 1687 Leibniz asked for the curve along which a particle may descend under gravity so that it moves equal vertical distances in equal times. Huygens showed that the semi-cubical parabola x^3 = ay^2 satisfied this property.

On the face if it, that statement is nonsensical—it says that the vertical component of a particle's velocity sliding down that curve is a constant.  But that can't be true.   Consider a particle released from rest from a point P on the curve.  The intial velocity is zero, and therefore the vertical component of the initial velocity is zero. Later on the particle picks up speed, so the vertical component of the velocity is nonzero.  We see that the vertical component of the velocity changes, so it cannot be a constant, contrary to the Mac Tutor's assertion.

I don't know the correct statement of Leibniz's question and Huygens' solution, but certainly Mac Tutor's formulation and dozens of duplications around the net are not it.

## Restatement of the puzzle...

Interesting puzzle.  Here is a clearer restatement.  I have not attempted to solve it.

 > restart;
 > with(plots):
 > display(         pointplot([[1,1], [2,1], [3,1], [4,1], [5,1], [6,1], [7,1]], color=black),         pointplot([[1,2], [2,2], [3,2], [4,2], [5,2], [6,2], [7,2]], color=red),         pointplot([[1,3], [4,3], [5,3], [7,3], [1,4], [4,4], [5,4], [7,4] ], color=yellow),         pointplot([[2,3], [3,3], [6,3], [2,4], [3,4], [6,4]], color=pink),         pointplot([[1,5], [3,5], [5,5], [7,5], [1,6], [3,6], [5,6], [7,6]], color=brown),         pointplot([[2,5], [4,5], [6,5], [2,6], [4,6], [6,6]], color=purple),         pointplot([[1,7], [2,7], [7,7], [1,8], [2,8], [7,8], [1,9], [2,9], [7,9]], color=blue),         pointplot([[3,7], [5,7], [3,8], [5,8], [3,9], [5,9]], color=green),         pointplot([[4,7], [6,7], [4,8], [6,8], [4,9], [6,9]], color="Orange"), symbol=solidcircle, symbolsize=50, axes=none);

Puzzle: Rearrange the color disks, by moving them up or down (not horizontally),

so that there remain no repeated colors in each row.

PS: I see that Christian Wolinski has already said the same thing.  Sorry for the repetition.

## Substitution with eval()...

@acer I thought about doing it that way at first, but did not want to risk it, fearing that eval() may do the two substitutions in sequence, which generally will yield the wrong result.  The help page on eval() says that the substitutions are made simultaneously, so that's reassuring. But in the next paragraph is says that "if there are symbolic dependencies between the expression and the point at which it should be evaluated that are considered unsafe, eval will return unevaluated".  I don't know the circumstances under which this may happen, that's why I chose to roll my own.

## Oops......

@Christian Wolinski Yes, you are right, and thanks for the correction.

## Where do we start?...

If you missed a class where your instructor showed how to write a Maple proc, then see if you can get class notes from a classmate, or better yet, talk with the instructor.

Asking someone to solve your homework problem is not quite the right way to go.  It's you who's supposed to solve that problem, not someone else.

## Clarify...

1. What do you mean by "defining the image in relation to a chosen base"?

2. How are the base and T related to the image?

3. You ask "what I'm doing wrong", but you haven't said what you are doing.

## No crash here...

I am using Maple 2021.2 on Ubuntu 20.04 (actually Ubuntu MATE 20.04).  I believe that my Ubuntu is entirely up to date. I have no crashing problems.

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