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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...

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:

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...

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.

> 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

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...

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, 

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)

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This post can be downloaded here:  Download May202012.mw

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!

But what can we say about

Maple does not evaluate it:

And perhaps it should not because of the alternating sign;

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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 .

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!