How to plot a dynamical system as x' = f(x,y,z) , y'=g(x,y,z) . z'=h(x,y,z) ?

e.g.    x'=(x z )/y - x - 1

         y'=x y - 5 x z + y

         z'=( x z^3 )/y+( z^2)/y+6z

Hello!

I am trying to solve the differential equation:

for , 

From the page:

http://www.maplesoft.com/products/system_requirements.aspx

it would seem like ubuntu 12.04 is not officially supported for Maple 16. Could someone from Maplesoft comment if there are plans to add support with perhaps a patch? or will we have to wait until Maple 17?

I need to update for certain sofware, but would want to make sure I can run maple in an uncompromised way.

thanks

Hi

I browsed the forums but could not find a solution to my problem. Ii have a system of differential equations; however, I have the solution to one of the functions as an integral of another function in the system, but since the solutions are all numerical I don't know how to implement this. Here's the system and what I tried at first

#######################

eq1 := diff(W(r), r) = -(1-beta*(W(r)-W0))*(M(r)+4*Pi*r^3*p(r))/(beta*r*(r-2*M(r)));

balle := proc (L) local K, a, i, c, J;
J := L;
 c := nops(J);
 while J <> K do
K := J;
for i from 0 to c-1 do
if J[i+1] < J[i] then
a := J[i]; J[i] := J[i+1]; J[i+1] := a
end if
end do
end do;
return J
end proc

I got the error "Error, (in balle) invalid subscript selector " even if L is a list. I don't understand. Could you help me, pretty please? 

Hi everyone.

I need to plot a graph of y against x for the solutions for values of t form 0 to 0.003 seconds using

c=50m/s

beta=10

A=0.01m

L=0.5m

The equation is y(x,t) = A*e^(-beta(x-L-ct)^2/(L^2))

I also need to show that the above equation can be a solution for (d^2y/dt^2) = c^2 * (d^2y/dx^2) on maple.

Cheers if anyone could help me with this.

On several occasions, while working with lists or Matrices, I have been drawn to using a combination of seq and if, as in the following:

seq(`if`(a,b,c), i = 1 .. 10 )

This appears to be a powerful approach. Unfortunately, I have not found much documentation on it.

I have been able to pattern-guess to a limited extent for my limited needs.

Would you know of a good place to go for information?

My understanding is: "a" is the conditional...

I have found very little help about the Generate command of the RandomTools package.

I also have minor gripes about the syntax. And what better way to deal with these than to voice them?

This is how I was able to generate random lists and random Matrices.

A list of 10 random integers between 1 and 100:

L := RandomTools:-Generate(list(integer(range=1..100),10));

      L := [47, 8, 46, 44, 9, 77, 59, 16, 1, 70]

Darts.mw

I think it was Acer who did the coding for a similar previous problem. I modified it to find the components of a set which sum to 150.

Why is it that it doesn't find all the solutions with {assume=nonnegint}. eg i have to run a additional pgm {assume=binary} to catch all solutions.

1. is there a procedure to catch all?

2. is there a way i can put the list and the desired sum in the input: eg SSP(...

http://en.wikipedia.org/wiki/Hodge_theory
H(M) = ker(d_k) / im(d_k-1)

would like to see the example of calculation of H(M) above

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.

I have been severely mystified by the following:
                                                                                                                      
I have...

why the command does not work: _EnvHorizontalName := x;_EnvVerticalName := y?

And a few lines later asks me the name of the axes

restart;
with(plots); with(plottools);

The circle S with center at the origin and radius 2 is given by the equation x2 + y2 = 4
The circle S have two tangents passing through the point (4, 1). Find the equation for each of them.
x^2+y^2 = 4;

subs(y(x) = y, solve(diff(subs(y = y(x), x^2+y^2 = 4), x), diff(y(x), x)));

Maybe I'm missing something but I thought boys surface was one surface and when I plot it in maple it appears to have two surfaces.

testing.mw

Hi all,

Basically, I want to substitute everthing in m using the s .

More or less, I am doing a reparameterization.

I have looked into subs command, but it does not quite does what I want.

It seems to me the Maple wont be substituting exp(-mu) to s1 ( or exp(mu) to 1/s1 ) if the exp has some other powers in it, such as exp(mu+tau).

Any ideas?

Thanks.

Casper