## How can I scale a differential equation in Maple?...

I am teaching a course in biofluid mechanics and am looking to help the students get more use out of Maple. Often it is advantageous to scale a differential equation (and initial conditions) using dimensionless variables to reduce the number of free parameters in a problem. For example, the simple linear oscillator differential equation:

Eq(1)         m*d2x(t)/dt2 + k*x(t)=0

where k and m are parameters.  If we define a dimensionless time, s=t/T, and a dimensionless position, X=x/L, where T and L are constants, , Eq(1) becomes

Eq(2)         (mL/T2 ) *d2X(s)/ds2 +  kL*X(s)=0

Then choosing T=sqrt(m/k) we arrive at

Eq(3)         d2X(s)/ds2 +  X(s)=0

which has no parameters.  Can this sequence be done in Maple for a differential equation...i.e. change of variables?

Thanks

## How to solve equation system?...

Hi,

i want to solve equation system u0(x,t),u1(x,t),v1(x,t),v0(x,t)v2(x,t) dependent on f(x,t).

I attached file.

worksheet.mwworksheet.mw

## How do I remove italics from axis labels?...

I am writing a textbook in biomedical engineering and using Maple 14 for generating figures.  In many of the graphs, my axis labels have subscripts or superscripts.  For example in a 2D plot statement I type   labels=[x,f[0](x)] which gives a subscript 0.   However, both x and f0(x) appear in italics.  How can I have them appear as normal...i.e. without italics? The labelfont command does not seem to have an instruction to remove the italics.  Can you assist me?

## NonLinearFit - Operator mode...

Hi!

Here below is the code I got problems:

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

Dens := proc(v)
local theta, r;
evalf[8](
Int(
Int(
4*r/(1-0.84*cos(theta)^2)^(1/2)*exp(-r*(6.25-5.245*cos(theta)^2)^(1/2))
, theta = 0. .. 2*Pi)
, r = 0. .. v)
) assuming v>=0
end proc;

#
#

FitFinalDens := NonlinearFit(
b*(1+a*u)/u*Dens(u/(1+a*u))
, depth
, veloc
, [u]
, initialvalues = [a = 1.4, b = 0.13]
, parameternames = [a, b]
, output = [leastsquaresfunction, residuals, parametervector]
, parameterranges=[a=1.1..3.0,b=0.02..0.8]
);

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

Then, I obtain two sort of errors:

First error message:

Error, (in Statistics:-NonlinearFit) invalid input: no implementation of NonlinearFit matches the arguments in call, 'NonlinearFit(0.13*(1.+1.4*u)*(int(int(4*r/..........

etc...

Second error message:

Error, (in Statistics:-NonlinearFit) complex value encountered

So, really I don't known how to correct the code.

I tried a lot  of things such as using  "value" command,  "Re" command, etc.

Do you have a solution?

Sincerely yours.

Jacqr

## procedure problem...

i wrote a procedure for determine a lambda symmetries and first integrals of ODEs.

Procedure is running but commands is getting error.

Can  anybody help me.

## unexpected string and procedure error...

i wrote a procedure to  find some functions but at the end  of the procedure gives unexpected string error. i didn't find any way out.

Best regards.

## Suggestions on how to check the progress of a proc...

Hello

I wonder if there is a way to see the progress of a specific procedure.  I have checked the forum for some answers and found that some of them propose a progress bar. However the progress bar doesn't seem to fit within a procedure.

I don't need anything fancy but I need to see the progress of the loop inside of the procedure (over 3,000,000 times).

Any suggestions?

Many thanks

PS. I am running Maple 2016 too but I would rather see a solution that works on Maple 14 too, if possible.

## How to retrieve only the monomials (no coefficient...

Hello

I wonder if there is a function to retrieve only the monomials from a multivariable polynomial in x, y and z. Below is one such polynomail.

theta[2]*x3*x0-theta[8]*x2*x1*x0-theta[2]*x2*x1-theta[6]*theta[2]*x2*x0^2-theta[4]*theta[2]*x2*x0-theta[2]*theta[7]*theta[10]*x1*x0^3+theta[8]*theta[2]*theta[9]*x1*x0^2-theta[2]*theta[5]*theta[10]*x1*x0^2-theta[2]^2*theta[3]*theta[10]*x0^3+theta[6]*theta[2]^2*theta[9]*x0^3+theta[4]*theta[2]^2*theta[9]*x0^2

and the result

[x3*x0,x2*x1*x0,x2*x0^2,x2*x0,x1*x0^3,x1*x0^2,x0^3,x0^2]

Many thanks

Ed

## Plot in a same graph ( a sequence of functions in ...

Hello,

I have a sequence of functions :  solution[i] , i = 1..n

I have a sequence of times:          Time[i], i = 1..n+1

I need help to plot in the same graph:

plot(  Sol[1] , t = Time[1]..Time[2] )

plot(  Sol[2] , t = Time[2]..Time[3] )

plot(  Sol[3] , t = Time[3]..Time[4] )

etc...

plot(  Sol[n] , t = Time[n]..Time[n+1] )

Thank you

using worksheet mode, is there a way to automatically color any comments after (#) with a different color than the default red?

I have been using Maple for years and did not need to significantly document or comment on my worksheets before because I only needed to share my worksheets with close collegues who have a lot of experience with Maple too. However, now I need to share my code with a general audience that might not be a Maple user. So I need to add enough comments after each line, and I have been manually changing the color of comments after the # to green to give the reader the indication that this is a comment and not part of the code, like this for example:

 > restart;
 > f:=(x,y)->sin(sqrt(x^2+y^2))/sqrt(x^2+y^2); # Define f as a function of the variables x and y
 (1)
 > df:=(x,y)->eval(diff(f(a,y),a),a=x); # Define df as the partial derivative of f with respect to x
 (2)
 > df(1,3); # Evaluate df at x=1, y=3
 (3)
 >

It would be great if Maple can automatically color comments like typical editors do. Is this possible? if not, does anyone have an advice for a nice easy way to add proper documentation to worksheets?

## Modeling of DC Motor. Problem with DiffEquation...

Hello,

I'm modeling the simple DC motor system in Maple.
The equations describing the system;

eq1:=J*diff(theta(t),t,t)+b*diff(theta(t),t)=K*i(t):
eq2:=L*diff(i(t),t)+R*i(t)=V(t)-K*diff(theta(t),t):
DCMotor:=[eq1,eq2];

First, I create the system using DiffEquation:

Sys:=DiffEquation(DCMotor,[V(t)],[theta(t)]);

And now I have problem. The input var is V(t) (input voltage) and the output var is theta(t) (position of the rotor).

But I wont to have in output var not position of the rotor but speed of the fotor - diff(theta(t),t)

How to set output var for diff(theta(t),t) (the speed of the motor)?

Best

Rariusz

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