## Why adding noise mu(t) to y_a not working in plot?...

5_6190449716501677775.pdf

I ahve a signal y_a to which adding mu(t) doesn't seem to give any plot but error , what is missing here?.

And also in second k(x,t) pdf file I want the value of k(x,t) after I did the integration. When I type k(x,t) and hit enter it's not giving me the value of k(x,t) but returns k(x,t) as it is.K(x_t).pdf

## how to use odetest to very series solution with ex...

I do not remember now if this was asked before. Doing search here is hard.

But I am trying this now on 2022.1 and this gives FAIL.

What is the correct syntax to use odetest to verify solution to ode using series method with expansion around infinity? Why do I get FAIL here?

 > interface(version)

 > Physics:-Version()

 > restart;
 > ode:=x^3*diff(y(x),x\$2)+x^2*diff(y(x),x)+y(x)=0; sol:=dsolve(ode,y(x),'series',x=infinity); odetest(sol,ode,'series','point'=infinity)

Warning, unable to compute series necessary to test the given solution

 >

Update

I've testsed methods given below on 6 random ode's using Maple odetest, VV method and Axel method. THis is the result obtained using Maple 2022.1

odetest was able to verify the solution zero out of 6 times.
VV method was able to verify the solution 3 out of 6 times.
Axel method was able to verify the solution 5 out of 6 times.

So based on this small test, Axel method seems to do the best. Attached worksheet. I will use this method to verify my series solution to ode's instead of Maple's odetest but will use Maple's odetest for non-series method solutions.

 > interface(version);

 > Physics:-Version();

 > restart;

Example 1  Regular singular point. Complex roots

 > Order:=6; ode:=sin(x)*diff(y(x),x\$2)+cos(x)*diff(y(x),x)+1/x*y(x)=0; sol:=dsolve(ode,y(x),type='series',x=0)

VV method

 > odetest(sol,ode): asympt(%,x);

odetest method

 > odetest(sol,ode,'series','point'=0);

Axel method

 > rhs(sol): Y:= unapply(%, x): eval(lhs(ode), y=Y): MultiSeries:-asympt(%, x): convert(%,polynom);

Example 2 Regular singular point. Dierence is integer

 > Order:=6; ode:=sin(x)*diff(y(x),x\$2)+cos(x)*y(x)=0; sol:=dsolve(ode,y(x),type='series',x=0):

VV method

 > odetest(sol,ode): asympt(%,x); convert(%,polynom);

odetest method

 > odetest(sol,ode,'series','point'=0);

 Axel method
 > rhs(sol): Y:= unapply(%, x): eval(lhs(ode), y=Y): MultiSeries:-asympt(%, x): convert(%,polynom);

Example 3 Regular singular point. Repeated root

 > Order:=6; ode:=(exp(x)-1)*diff(y(x),x\$2)+exp(x)*diff(y(x),x)+y(x)=0; sol:=dsolve(ode,y(x),type='series',x=0):

VV method

 > odetest(sol,ode): asympt(%,x): convert(%,polynom);

odetest method

 > odetest(sol,ode,'series','point'=0);

 Axel method
 > rhs(sol): Y:= unapply(%, x): eval(lhs(ode), y=Y): MultiSeries:-asympt(%, x): convert(%,polynom);

Example 4 Regular singular point. Repeated root

 > Order:=6;   ode:=(exp(x)-1)*diff(y(x),x\$2)+exp(x)*diff(y(x),x)+y(x)=0; sol:=dsolve(ode,y(x),type='series',x=0):

VV method

 > odetest(sol,ode): asympt(%,x): convert(%,polynom);

odetest method

 > odetest(sol,ode,'series','point'=0);

 Axel method
 > rhs(sol): Y:= unapply(%, x): eval(lhs(ode), y=Y): MultiSeries:-asympt(%, x): convert(%,polynom);

Example 5 . Regular singular point. Complex roots

 > Order:=6;   ode:=x^3*diff(y(x),x\$2)+sin(x^3)*diff(y(x),x)+x*y(x)=0; sol:=dsolve(ode,y(x),type='series',x=0):

VV method

 > odetest(sol,ode): asympt(%,x); #convert(%,polynom);

odetest method

 > odetest(sol,ode,'series','point'=0);

 Axel method
 > rhs(sol): Y:= unapply(%, x): eval(lhs(ode), y=Y): MultiSeries:-asympt(%, x): #convert(%,polynom);

Error, (in MultiSeries:-multiseries) need to determine the sign of -I*3^(1/2)

Example 6 . Regular singular point. Complex roots

 > Order:=6;   ode:=x^2*diff(y(x),x\$2)+x*diff(y(x),x)+(x+1)*y(x)=0; sol:=dsolve(ode,y(x),type='series',x=0):

VV method

 > odetest(sol,ode): asympt(%,x); #convert(%,polynom);

odetest method

 > odetest(sol,ode,'series','point'=0);

 Axel method
 > rhs(sol): Y:= unapply(%, x): eval(lhs(ode), y=Y): MultiSeries:-asympt(%, x): convert(%,polynom);

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## Maple's WeierstrassP vs Weierstrass' P-function...

What is the [explict] relation between Maple's WeierstrassP and Weierstrass' P-function (e.g. https://en.wikipedia.org/wiki/Weierstrass_elliptic_function) ?

## Specify unit system?...

How can I specify english units as the default in Flow?  Rather than Newtons (N), pound force (lbf)?

## Expecting numerical value from Integrate but getti...

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Want to integrate x*f(x) where x is from -20..20, I am expecting a pure float number but getting symbols like statevalf_pdf in answer.

## Is there a way to differentiate between errors?...

I am using some custom procedures which return error messages if something doesn´t work as planned and would need to make a distinction (when using try..catch) between these errors and all the other potential error messages Maple can return. Is there a way to do this efficiently - without having to list all of the error messages from my own procedures after catch?

## RK-4 for System of Nonlinear ODE'S...

Hello Everyone;

Hope you are fine. My problem is convert into nonlinear system of ODE's and further i need make the code of apply rk-4 for the formulated ODE's. Kindly guide me. The file is attached. I am waiting for your kind response.

Thanks

Question3.mw

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## How to have Maple solve this simple ODE?...

The worksheet here shows a couple of failed attempts at coaxing Maple to calculate the general solution of a pretty simple second order ODE.  I have also included the expected solution which I  have calculated by hand.  Perhaps I am missing a key trick.  Any ideas?

The ODE that I am actually interested in is significantly more complex. The one in the worksheet is a much simplified "bare bones" specimen that exhibits the issue that I am facing.

Attempt to solve with Heaviside

 > restart;
 > de := diff(u(x),x\$2) = Heaviside(x - a)*u(x);

dsolve fails:

 > dsolve(de);

Attempt to solve with piecewise

 > restart;
 > de := diff(u(x),x\$2) = piecewise(x < a, 0, 1)*u(x);

 > dsolve(de);

Error, (in dsolve) give the main variable as a second argument

 > dsolve(de, u(x));

Error, (in dsolve) give the main variable as a second argument

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The solution is easy to calculate by hand

We just solve the (quite trivial) DE over the intervals  and x>a

separately, and patch the two solutions by requiring the continuity

of  and  at .  We get

 > sol := piecewise(x < a,         x*c[1] + c[2],         ((a*c[1] + c[1] + c[2])*exp(x))/(2*exp(a)) + ((a*c[1] - c[1] + c[2])*exp(-x))/(2*exp(-a)));

## Select Values in Matrix...

Hello,

I am fairly new to Maple. Suppose I have two Matrices

A := <<true, false, true> | <true, false, true> | <false, false, false>>

B := <<1, 2, 6> | <3, 4, 7> | <22, 33, 44>>

and apply select(A, B)

Why do I receive [[[(),3,22],[(),(),()],[(),7,44]]] instead of [[[1,(),6],[3,(),7],[(),(),()]]] as a result? I just want to select every element of B where A is true.

I appreciate any insight.

## algebra,factoring...

This is a simple algebraic, but I would like to know how to officially solve the problem,

I tried factor(6*a+12*b+18*c); it simply outputs what I input.

I tried primpart(6*a+12*b+18*c) ; the output is: a+2b+3c

I tried content(6*a+12*b+18*c), the output is 6

What I'm looking for an output is, 6*(a+2*b+3*c), this is the answer my Algebra book is looking for, I also get this answer by

using my HP Graphing Calculator, but I'm unable to get the answer from Maples. Can anyone help?

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## Who invented the inverse model approach?...

Inverse kinematics can be done in several ways (this webinar gives a very good overview https://www.youtube.com/watch?v=X0OZ9EM6dns). A effective and simple method is to run a model in reverse direction. This can’t be done with causal modeling tools, where information flow is fixed by design (https://de.maplesoft.com/support/help/MapleSim/view.aspx?path=MapleSimUserGuide/Chapter01).

Inverse kinematics, which is possible with acausal modeling tools, is only an example for running a model in the reverse (i.e., inverted) direction.

Without success, I tried to find a reference who first came up with that elegant approach.

Anyone knows more?

## complex numbers...

Hi

I have a problem with calculating complex numbers in Maple.

I type forexample 8(cos(Pi/2)+I*sin(Pi/2)) and I get 8, I should get 8I

Should I re-install Maple or edit my settings?

best regards

## solve equations...

Hi everybody,how can I solve these equations in Maple and plot the answers? tnx...

eq1 := diff(x(t), t) = 35*(y-x)

eq2 := diff(y(t), t) = -x*z-7*x+28*y

eq3 := diff(z(t), t) = x*y-3*z

## How can I extract the coordinates from spacecurve...

Hi Dear All,

I need to extract the coordinates from spacecurve commend. For example;

h3:=spacecurve([-x,-y,z],omega=ws..0,color=green,thickness=5):
h4:=spacecurve([-x,y,z],omega=ws..0,color=blue,thickness=5):

Where, omega is a parameter difinening x, y, z.

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