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How can one use maple to linearized nonlinear ODE of this type

with maple.

Best regards.




  Suppose I have the following code




solve({f[1], f[2]}, {x1, x2}):
a,b:= eval([x1, x2], %[1])[]:
a, b;



It could work and give me "1 and -1". 


I would like to have a general subroutine, solving f[1]...f[n]. I cannot input  "solve({f[1], f[2],....,f[n]}, {x1, x2}):" just like that. Is ther any way to use "solve" or similar module to handle arbitary number of variables?

I am trying to use solve to determine 5 unknowns from 12 equations each with seperate data points); however, maple requires you to have equal number equations and variables. Is there any way around this?

There are two ways of expressing the solution to a cubic equation, one of them uses cos and arccos [1]. How do I / is there a way to ask Maple to get this form?

More generally, can Maple be instructucted to solve equations using trig identities?


I am fitting polynomial differential equations to data, and I came across some troubling behavior. I have sets of coordinates in x, y, z, and values w at these coordinates. The x,y,z coordinates and the data at these coordinates are concatenations of three subsets of data each, and depending on the order of the concatenation, I get different polynomials from the stats fit command. The difference is not trivial -- it makes a huge differentce in the stability of the differential equations. I have written a demonstration worksheet to show this problem.

John Starrett

Solve IVP with complex coef. with compplex varables numerically..

the sys. is x'=-iDelta1x(t)+y(t)+epsilon


z'=-2(x*(t)y(t)+x(t)y*(t)), where * means complex conjugate 

I solve it as:


dsys :={diff(x(t),t)=-I*Delta1*x(t)+y(t)+epsilon, diff(y(t),t)=-I*Delta2*y(t)+x(t)*z(t), diff(z(t),t)=-2*(conjugate(x(t))*y(t)+conjugate(y(t))*x(t))}:
functions := indets(dsys, anyfunc(identical(t))):
redefinitions := map(f -> f = cat(op(0, f), _R)(t) + I*cat(op(0,f), _I)(t), functions):
newsys := map(evalc @ Re, redefinitions) union map(evalc @ Im, redefinitions):

incs := {x_R(0)=0, x_I(0)=0, y_R(0)=0, y_I(0)=0,z_R(0)=-1/2, z_I(0)=0}:
dsol1 :=dsolve({newsys,incs},var,numeric, output=listprocedure, abserr=1e-9, relerr=1e-8,range=0..1):

but it seems there is not runing propebly


If we a complex number in Maple, like for example:



How can we make maple rewrite it like this?



I tried using the comands Re(%) and Im(%) but Re just gives the whole expression again and Im gives 0.


I have a excel spreadsheet with a number of data points which I want to plot in Maple.  I have imported the data and I did manage to produce a point plot, but how can I exclude some of the data points when I plot the point plot?
I would, for example, like to exclude the negative values and only plot the data which is greater than zero.


I am relatively inexperienced with Maple and would like to either be pointed in the right direction or shown a similar example to my problem for reference.

My problem is I need to write a programme using the below equations



I then have to use the below values to show my programme works






After proving it works I have to apply it to a mass spring system using realistic parameters. Using visual and analytical ways to show findings.



when x and y are the displacement from the equilibrium. Initially the masses are displaced from their equilibrium posistions and released so that

x(0)=a, y(0)=b, Dy(0)=Dx(0)=0

then repeat with different smaller calculations

Any help would be much appreciated


When I write in maple the following:



What do I need to write to make maple make the operation that will evaluate the expression and show the following?




simplify(%) or evaluate(%) only shows it the same way it was inputted to start with.



  I have the following code for using "PolynomialSystem" solve equations of polynomial




f:=PolynomialSystem({x+y-3, x^2+y^2-5}, {x, y}):




The output is


x, y
{x = 2, y = 1}, {x = 1, y = 2}
{x = 2, y = 1}
{x = 1, y = 2}
x = 2
y = 1
x = 2, y = 1
-x = -2.
-y = -1.


From what I have seen, I cannot subtract the values of x and y as 2 and 1. Is there any way that I can get the values of solutions of variables, namely I can assign a variable "a" as 2, and the other variable "b" as 1?


Thank you very much!





How can one deduce values of f(eta), diff(f(eta),eta) and diff(f(eta),eta$2) from values of f1,f2,f3,f4,.. in the results of the finite difference here . I need the outcome for f and its 1st and 2nd derivatives as listed above. Please help.

How do I compute the Lyapunov exponents for Lorenz system

Is it possible to organize output of plots in Mathematica-like manner

in one list (placed in one cell)?

In Maple I use tables for these purposes:


Maybe, does there exist a more elegant solution?

hi...plese help me


how i can solve set of non linear differential equation with a unknown parameter with numeric role in maple software??

thank a lot ...

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