Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

Hey

 

Is it possible to draw a slope field for a second order differential equation with initial conditions?

 

Hi

I am asking for your help, as I would like to know if it's possible to integrate a function using SI-units.

This is what I get when I try:

Copied directly:

with(Units[Standard]);
∫10 ⟦m⟧/(⟦s⟧^(2))ⅆ⟦s⟧
Error, invalid differential
                       /      (m)                         
Typesetting:-mambiguous|int10 ----Typesetting:-mambiguous(
                       |         2                        
                       \      (s)                         

                                                                \
  DifferentialD(s), Typesetting:-merror("invalid differential"))|
                                                                |
                                                                /

 

 

Why 3D .eps figures produced by Maple 2020 are often excessively large?

So, it´s a little heavy to the viewer and to compile to PDF.

  • How could we reduce the size without losing any quality? 

Is the following function w 

equal to next functions for a=1 or a= -1?

if a=1 then 

w=

if a=-1 then 

w=

where n>1, B,c and k are arbitrary constants.

################################ 
restart:
a:=-1:
B:=0:
c:=2: 
h:=1:

#assume(n>1):
n:=3:
assume(0<=x and x<h):
assume(0<=t and t<h):  

a:=-1:
if is(a>0)=true then
omega:=(x,t)->((2*c*n/(a*(n+1)))*(sin ((x-c*t+B)*sqrt(a)*(n-1)/(2*n)))^2 )^(1/(n-1));
print(omega(x,t));
elif is(a<0)=true then 
omega:=(x,t)->(-(2*c*n/(a*(n+1)))*sinh ((x-c*t+B)*sqrt(-a)*(n-1)/(2*n))^2 )^(1/(n-1));
print(omega(x,t));
end if:

plot3d(omega(x,t),x=0..1,t=0..1);
################################

################################
restart:
a:=-1:
n:=3:
c:=2:
r:=0:
k_1:=0:
k_2:=0:
h:=1:

n:=3:
assume(0<=x and x<h):
assume(0<=t and t<h):  
if a=1 then
  omega:=(x,t)->piecewise(abs(x-c*t)<=2*n*(k_1-r)*Pi/(k_1*(n-1)),(sqrt(2*c*n/(n+1))*sin ((x-c*t)*(n-1)/(2*n)+r*Pi/k_1))^(2/(n-1)),0);
print(omega(x,t));
elif a=-1 then
  omega:=(x,t)->(sqrt(2*c*n/(n+1))*sinh ((x-c*t)*(n-1)/(2*n)+k_2))^(2/(n-1));
print(omega(x,t));
end if:


plot3d(omega(x,t),x=0..1,t=0..1);

 

Hi I have a transfer function first or second order and I want to get it into standard form

Which the transfer function is

of H(s)/(W__I(s) so how height of a tank (H) is affected by incoming flow rate (W__i(s)) but I need to get this transfer function into standard 1st order form

Where I need to find what K and tau are to get it in to this form and tau is always in the units of time. How can I do this in maple? It's pretty impossible by hand I find. I've attached my workbook for it.

General_form.mw

Hi,

I am doing some analyses of autonomous DEs (single equation and systems). Maple is able to easily produce 2d- and 3d-phase protraits for systems. However, I am struggling to produce 1d-phase portrait for autonomous first-order DEs. I would like to produce a single axis with some labels and decorations which include the following:

  1. All equilibrium/critical solutions of the DE.
  2. Arrows on the axis indicating if the non-equilibrium solutions are increasing or decreasing in a certain interval.

For example, for dy/dx = -y^2*(5*y-1)^2, would like to produce the plot in the attached file. 

How might I achieve this?

1d-phase_portrait.pdf

helle to your all

 

as i can see there are functions to show steps of a calculation

such as ExpandSteps() and ShowSolution()

but would it not be possible to use these or some other function to show steps of the function called isolate()

it should be trivial since most online calculators are able to do this. and so does maple in the back - we just don't see the steps only the result

 

thanks regards mikkel

 

RootOfQuestion.mw

Hi Everyone, so i understand (to the best of my knowledge) the purpose of RootOf and I have worked with them before but now for some reason when i try to use allvalues to express the solution explicitly it does not express it, instead just keeps as RootOf expression. 

I have attached the maple file I am working with. 

I have also tried solve(expr, explicit) as well as convert(expr, radical) and still nothing. 

Am I missing something small? 

How to plot the phase portrait of the system of fractional DEs?

0< nu<1

Consider the infinite product

(1-qi)(1-qiz-1)(1-qi-1z)

For i > 0

How would I expand this into a power series in qz in Maple? Say I would like the coefficient of q6z2

Or how would I get the first n terms up to some order of qz?

Dear Users!

Hope everyone fine here. I want to collocate Vector IntXYZ1 and IntXYZ2 present in file Q1 in such a way that the first M1M2 + 2(M3-1)M2 + 2(M3-1)(M1-2) rows are zero and other rows are collocated at x=(i-1)/(M1-1), y=(j-1)/(M2-1), t=(k-1)/(M3-1) for i = 2,3,…,M1-1, j = 2,3,…,M2-1, k = 2,3,…,M3 as given as XX (of order 27 by 27 with first 25 rows are zero) for M1=M2=M3=3

I am waiting for positive response to fix this issue. Thanks in advance

Q1.mw

I  am trying to find the integer numbers a, b, c, d, m so that the equation

(x−a)(x−b)(x−c)(x−d)=m

where a+d=b+c  and m≠0 has four integer solutions.

I found this equation randomly
solve((x-5) (x-3) (x+6) (x+8)=504, x);
How to find number a, b, c, d, m so that the equation
(x−a)(x−b)(x−c)(x−d)=m
has four integer solutions?

I am still a novice of Maple, but I want to carry out recurvive applications of some formula that involves non-commutative operators X and Y ([X,Y] = XY-YX). I used the following code, but I do not know how to tell Maple a rule that [X,X] = [Y,Y] = 0:

with(Physics);
Setup(mathematicalnotation = true);
Setup(noncommutativeprefix = {X, Y});

Z := X + Y + (1/2)*Commutator(X,Y);
subs(X=Y,Z);

The output is like this:

> Z := X + Y + (1/2)*Commutator(X,Y);
                          Z := X + Y + 1/2 [X, Y][-]

> subs(X=Y,Z);
                              2 Y + 1/2 [Y, Y][-]

The above [Y,Y] must be interpreted as zero, of course.

Thank you very much.

Hi,

How to remove the first column from my Tabulate command ?

SYRACUSEFina.mw

Thanks

The simple test procedure P constructs a large matrix.
Measuring the real time twice  (t1 and t2), t2 was by about 25% larger!
Now, if we remove the comment  before "Start",  t1 increases by 25% and t2 ~ t1.
So, the timing depends on whether some output is already on screen (standard interface).
Can you explain this?

restart;
P := proc(n,A)
  local i, j;
  for i from 1 to n do  for j from 1 to n do
    A[i,j]:=sin(arcsin(1/i-1/j+1/n))-1/i+1/j-1/n+i+j
  od od;
  NULL  #A;
end proc:

# "Start";
n := 300:
s := time[real]():
A:=Matrix(n,datatype=float[8]):
P(n,A):
t1:=time[real]()-s;

s := time[real]():
A:=Matrix(n,datatype=float[8]):
P(n,A):
t2:=time[real]()-s;
t2/t1;  # 1.24   WHY?

(For one of my programs, I found t2/t1 = 1.7)

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