by: Maple

## How to apply Homotopy operator for inversion of di...

Suppose I have an expression like

Is it possible to reverse the divergence expression using homotopy operator to obtain Psi and Phi?

The above divergence expression is possible since Euler operator of the left side is zero.

## What is causing this error with InitialValueProble...

I'm trying to approximate the solution of an IVP using Euler's method in the InitialValueProblem command and I keep getting this error (see attached worksheet). Can someone explain why? Thanks!

## Konigsberg Graph?...

Hello I'm having trouble create Konigsberg Graph on Maple. Here's the picture. Sorry if it's not clear enough. Thanks!

## Eulers method plot ...

Hi,

The question:

Create a table of the droplet´s range as a funstion of the initial velcity for v0=0.2..4 m/s in steps of 0.2 m/s, each with starting angle of 36 degree. What range of Reynolds numbers does this correspond to? Plot the result.

I get the result for one of the v values, but struggling to get values for all the v-values.

F_D:=proc(v::list) #force/mass
local k,vx,vy;
vx:=v[1];
vy:=v[2];
k:=-evalf(3*Pi*mu*d/m);        #common constant, calculated only one time
[k*vx,k*vy];                           #returns a vektor
end proc;

Euler:=proc(vo::list,h)             #using the Euler method to solve the equations
local vx,vy, F;
F:=F_D(vo);
vx:=vo[1]+h*F[1];
vy:=vo[2]+h*(F[2]-g);
[vx,vy];
end proc;

## Solving ODEs without the Student package...

As it says in the title, I would like to solve the following ODE numerically using forward Euler method, without using the Student Package.

(dy(t))/(dt)=t(1-0.3t)-(ty)(1+0.6t)

with initial condition y(0)=1. I want to solve it for up to t=1, and then plot both the solution by Euler's method and the solution by "dsolve" on the same graph so I can compare them.

Also, can I make a separate DEplot with t extending to 5?

## Plot Interface and Euler Angles...

Can someone explain to me, if you can, how the Euler angles on the plot interface work?

It looks like Phi is the rotation around z, Theta is the rotation around x, and Psi is around y. I'm trying to use matrices to compute the vector that is pointing towards your face as you're looking at the plot with the given Euler angles.

X := Matrix(3, 3, {(1, 1) = 1, (1, 2) = 0, (1, 3) = 0, (2, 1) = 0, (2, 2) = cos(phi), (2, 3) = sin(phi), (3, 1) = 0, (3, 2) = -sin(phi), (3, 3) = cos(phi)});

Y := Matrix(3, 3, {(1, 1) = cos(theta), (1, 2) = 0, (1, 3) = sin(theta), (2, 1) = 0, (2, 2) = 1, (2, 3) = 0, (3, 1) = -sin(theta), (3, 2) = 0, (3, 3) = cos(theta)});

Z := Matrix(3, 3, {(1, 1) = cos(psi), (1, 2) = sin(psi), (1, 3) = 0, (2, 1) = -sin(psi), (2, 2) = cos(psi), (2, 3) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 1});

and computing X*Y*Z*e3

TIA!

## Weird loop output limit, need assistance...

I am a student taking differential equations and I need to implement Euler's method using Maple 17. I have set up a do loop that looks like this:

`for i from 1 to n1 do`
`k:= f(t,v):`
`v:= v + h*k:`
`t := t + h:`
`od:`

Where n1 is initialized to 50, f(t,v) := 0.0207v2 -893.58, and h is 0.1. v and t are both initialized as 0.

## How to I create the Runge-Kutta's and Euler's meth...

Hi, I got a doubtI don’tknow how to make the Runge-Kutta’s and Euler’s method. The Runge-Kutta for thesecond and fourth order. I don’t know how to beginning the algoritms, I needsome help. Thanks.

## Help getting rid of a recursive assignment message...

I am trying to write out a code to solve for current in a LRC circuit. I have written a code that I think is capable of doing this but keep getting a recursive assignment message in my for loop. I have looked it over about a hundred times and can't see where I have defined a variable in terms of itself. Any help on this would be greatly appreciated. A copy of my code so far is listed below.

`> with(plots);> u := proc (t, Q, dQdt) options operator, arrow; 0.15e-2*cos(omega*t...`

## How to find roots of complex number...

Hi

So the question is to find complex number W from :

.

but I want the answer in polar form using e (Euler's number).

The question is specific to ask for the complex number W that lying in the first quadrant and having the largest possible real part. I calculated and got :

## Multibody System Modelling using Euler Lagrange Eq...

I am trying to model a multibody system using euler lagrange equation. There are 3 links in the system attached with each other by revolute joints. The first link has one end fixed with the revolute joint.

Angle with x axis=Theta1,Theta2,Theta3

Moment of Inertia = M1,M2,M3

I am not able to find the solution of ODE system comprising of 3 ODEs which I get after solving Euler Lagrange Eq for...

## How do I plot Euler and Runge Kutta plots on one g...

I'm using the commands:

RungeKutta(d/dt(y(t))=-y(t),y(0)=1,t=1,submethod=rk4,output=plot,numsteps=10);

Euler(d/dt(y(t))=-y(t),y(0)=1,t=1,output=plot,numsteps=10);

Each of these commands yields its own serperate graph.  How can I plot both on graph to see how the approximations vary?

Thanks!

## Euler's Method problem...

How do you enter h in a Euler's method problem? I need to change h=0.1 to h=0.05

I'm using the 2D input in Maple 14.

So far I have this:

> DE2 := diff(y(t), t) = 3+t-y(t);

> Euler(DE2, y(0) = 1, t = .4);

> Euler(DE2, y(0) = 1, t = .4, output = Error);

> Euler(DE2, y(0) = 1, t = .4, output = information);

## help with syntax error...

EulerSystem:=proc(f,g,n,h,tinit,xinit,yinit,t,s,y);
local i;
t[0]:=tinit;x[0]:=xinit; y[0]:=yinit;
for i from 1 to n do
t[i]:= evalf(tinit+h);
x[i]:= evalf(xinit+h*f(tinit,xinit,yinit));
y[i]:=evalf(yinit+h*g(tinit,xinit,yinit));  od;  end;

When i tried to execute maple dispayed "unable to parse" but i can't find out where the syntax error is.  "local" was the word with the red dotted line box around...

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