# Items tagged with constantconstant Tagged Items Feed

### How to draw a phase curve of ODE system?...

March 08 2013 by Maple

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Hey, I have a system of ODE and I can't draw it's phase curve. I tried to use DEplot and phaseportrait, but it doesn't work. Here is my system:

dx/dt=x

dy/dt=ky              (k is a constant)

Here is my piece of code:

DE := [diff(x(t), t) = x(t)];

DF := [diff(y(t), t) = k*y(t)];

with(DEtools);

phaseportrait([DE, DF], [y, x], t = -5 .. 5, y = -5 .. 5, x = -5 .. 5, k...

### Plotting with a constant

March 07 2013 by

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Hello, I have a problem with plotting graphs with a constant.. I have one system of equations and one another equation:

dx/dt=x(t)

dy/dt=ky(t)

and

|y|=C|x|^k

I need to compare theit curves.

k and C are constants. I thought it is alright if I would remove constants, BUT there is one in the power, so I have no idea what to do..

I just tried to plot the system, but it doesn't work either:

### What kind of constant is _Z1~, used...

November 25 2012 by

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Thanks a lot Markiyan, and I am sorry I may have overlooked this already answered question. But, now I have just one more thing to know. On using AllSolutions = true in solve I get the answer as x = _z1~ ∏ / k, I then try to subs my fav symbol N instead of _Z1~, but Maple doesn't take it! It keeps it as it is. What kind of constant is this _Z1~, I had thought it to be the same as _C1, which is used by Maple while solving any ODE.

Reason why I want to...

### Some Identities from the MRB constant

November 22 2012 by Maple

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As many of you know now the MRB constant = sum((-1)^n*(n^(1/n)-1),n=1..infinity).

Here are some equations involving various forms of that summation.

The first one involves convergent series and is too obvious. The others involve divergent series.

The last two, however, are new!

Let c=MRB constant and a, c~, x, and y = any number.

sum((-1)^n*(c~*n^(1/n)-c~),n=1..infinity)= c*c~.

evalf(sum((-1)^n*(n^(1/n)-a),n=1..infinity)) gives c-1/2*(1-a).

evalf(sum((-1)^n*(x*n^(1/n)+y*n),n=1..infinity)) gives (c-1/2)*x-1/4*y.

And it appears that

evalf(sum((-1)^n*(x*n^(1/n)-a),n=1..infinity)) gives (c - 1/2)*x + 1/2*a.

### Convert D operator to "diff" form

September 09 2012 by Maple 16

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> f := a+D(x);

> convert(f(t), diff);

Is there a way to tell Maple that "a" is a constant, so (t) won't attach to a? thanks, kyle

### Computing the MRB constant in Maple...

July 14 2012 by Maple

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The MRB constant can be computed in Maple by evalf(sum((-1)^n*(n^(1/n)-1),n=1..infinity)).

On my laptop restart; st := time(); evalf(sum((-1)^n*(n^(1/n)-1), n = 1 .. infinity), 500); time()-st gives a timming of 37.908 seconds.

Using the procedure posted at the bottom of this message st := time(); A037077(500); time()-st gives a much faster timing of 1.903 seconds.

My fastest timing for 500 digits of MRB comes from my...

### The best approximations to the MRB const...

June 09 2012 by Maple

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A better approximation gives more digits of accuracy in the result per digit of precision used in the computation than a good approximation does.  I was wondering if anyone could come up with a better approximation to the MRB constant than 31/165,

### MRB constant Z

May 26 2012 by Maple

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The MRB constant Z will probably have several parts.

The following example is from the Maple help pages> with(GraphTheory);> with(SpecialGraphs);> H := HypercubeGraph(3);
DrawGraph(H)



What I would like to do in the MRB constant z,  MRB constant z part2, and etc. is to draw a series of graphs that show the some of the geometry of the MRB constant.

See http://math-blog.com/2010/11/21/the-geometry-of-the-mrb-constant/. I would like to draw a tesseract of 4 units^4, a penteract of 5 units^5, etc and take an edge from each and line the edges up as in Diagram 3:

 >

 >

### MRB constant N part 3

May 21 2012 by Maple

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Below we have approximations involving the MRB constant. The MRB constant plus a fraction is saved as P while a combination of another constant is saved as Q. We then subtract Q from P and always have a very small result!

### MRB Constant Y

April 28 2012 by Maple

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### MRB Constant X

April 21 2012 by Maple

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The MRB constant is evaluated by

### MRB Constant W

April 14 2012 by

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 (1)

What are the quotients  ot the  continued fration of the sum of

Here are the  quotients  of some partial sums.

 (2)

 (3)

 (4)

 (5)

 (6)

 (7)

 (8)

 (9)

 (10)

 (11)

 (12)

 (13)

 (14)

Here are the quotients of the  continued fration  of the sum.

 (15)

With the exception of the leading 0, that is close to the integer squence of pi.

 (16)

The exponents of 2 that sum the numerator and denominator, in the following way, of that multiple of pi give rise to the integer sequences {0,1,2,3,8,16},numbers such that floor[a(n)^2 / 7] is a square, and {0,2,3,4,8,16},{0,3} union powers of 2.

 (17)

We can do the same thing for the first 20 quotients giving rise to the integer sequences {0,1,2,5,6,8,10,13,17,19,22,23,24,28,31} and {0,4,6,9,12, 14,15,16,18,22, 23,24,28,31}. What can be said of these sequences?

 (18)

 (19)

 (20)

### MRB Constant V

March 23 2012 by Maple

But what can we say about

Maple does not evaluate it:

 product: Cannot show that (-1)^n*(n^(1/n)-1) has no zeros on [2,infinity] (1)

And perhaps it should not because of the alternating sign;

 (2)

 (3)

 (4)

### MRB constant U

March 18 2012 by Maple

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If you use all the convergents of the simple continued fraction of the MRB constant as the terms of a generalized continued fraction, then likewise use the new convergents in another generalized continued fraction, and so on... you arrive at 0.5557531....  For more on this process see https://oeis.org/wiki/Convergents_constant .

### How to Solve a First-Order IVP Involving...

October 29 2011 by

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Hi,

I've figured out several ways to accomplish this, using a series of commands, but is it possible using only dsolve to solve a first-order ivp involving two constants: the constant of integration and a constant of proportionality. For example, the type that arise using Newton's basic law of heating/cooling:

y'(t) = k*(y(t)-10), y(0)=70, y(1/2)=50

I welcome all ideas, especially if there is something easy I'm missing, thanks!

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