MaplePrimes Questions

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Nothing to add

Actually I want to ask something else.

 

 

(Maple 2015)

For the simple ODE with initial condition
dsolve({ diff(y(t),t) = y(t)^2 - y(t)^3, y(0) = 1/10 }, y(t));

dsolve produces two different answers, almost randomly (even after restart or after closing Maple and reloading the worksheet). Namely:

(1)

(2)

or

(2')

but this simplifies to (2), so it's not a "true" bug.

Notice that (2) is correct but (1) is incorrect even for t=0 (the initial condition!):

evalf(eval(RootOf(-ln(_Z)*_Z+ln(_Z-1)*_Z-ln(10)*_Z-ln(9/10)*_Z-I*Pi*_Z+_Z*t-10*_Z+1),t=0))=1/10;

Maple seems to prefer the wrong solution (1) but occasionally produces (2) e.g. in a new whorksheet!
In earlier versions it seems that only (1)  appears.

The same ODE with another IC

dsolve({ diff(y(t),t) = y(t)^2 - y(t)^3, y(0) = 1/100 }, y(t));

 

evalf(eval(%,t=0));

 

is always incorrect. It should be

 

but Lambert's function never shows up!
Let me mention that only the exact solutions are affected, numeric is ok.

Without an initial condition, dsolve always uses LambertW:

dsolve({ diff(y(t),t) = y(t)^2 - y(t)^3}, y(t));

 

 

Can you explain this behavior?

 

 

Dear Friends

My problem is related to exporting Maple code to Latex, to be more specific I want Latex output that look exactly same as it appears in Maple worksheet like like Red Maple prompt etc.

I have found another solution to this:

"In file menu go to “Export As”, then save file in Tex format. But in order to run this Tex file you need to have files like maple2e.sty, mapleenv.sty, maplestd2e.sty, mapletab.sty, mapleenv.def, mapleplots.sty, maplestyle.sty, mapleutil.sty(all part of package maplestd2e), these all file can be copied from C:drive where maple is installed, just copy all these file to Latex folder and you can run Tex file exported from Maple."

But this do not give exactly what I want.

Please see Maple file and its exported Tex version(Not possible to upload) along with pdf output for Maple worksheet.

Maple_Export_to_Latex.pdfMy_Paper_on_Zakharov-Kuznetsove_equation_(Simplified_determining_equations_for_classical_symmetries).mw

Let A and B be two lists of monomials. I want a new list C contained that monomials of A where not divide by any monomial of B. For example if A=[x,y,x^2y,xy^2,y^2] and B=[x^2,y^3] then C=[x,y,xy^2,y^2].

I am getting the following expression when I partially differentiate an expression:

PDE11 := diff(theta(z, p), z, z, p)+2*lambda(p)*theta(z, p)*(diff(lambda(p), p))+lambda(p)^2*(diff(theta(z, p), p))+lambda(p)^2*(sin(theta(z, p))-theta(z, p))+2*p*lambda(p)*(sin(theta(z, p))-theta(z, p))*(diff(lambda(p), p))+p*lambda(p)^2*(cos(theta(z, p))*(diff(theta(z, p), p))-(diff(theta(z, p), p)))

I differentiate the above equation to get each term in the form of :table([f=......])

(table([f = 1+sum(Lambda[n](0)/factorial(n), n = 1 .. infinity)]))(p)^2

It is difficult to understand the expression. Maple does not show any error. Can you please tell me what the error is?

Hi, I am trying to find adomian's polynomial of exp(y), but after execution it shows DF(e^y), D^2F(e^y) as it is. why it does'nt show its derivative?plz help meNewADP.2.mw

Hi, I am working on an assignment and I am having difficulties with this Eurler method since I am working with vector.

The assignment:

If the aircraft's engine transmits power P to the air, the force of the propellar, Fp, satisfies P=Fpv. Since the force Fp acts in the direction of motion, it can be written in vector form as: (what I have so far)


with(linalg);

v:=Vector(2,1,[vx,vy]); velocity vector

nu:=v->Norm(Vector(v),2); (length of v)

Fd:=-1/2*C*rho*A*nu*v # air resistance

Fl:=1/2*Cl*rho*A*nu*v # liftforce in y direction here v=[-vy,vx]

Fp:=(P/nu^2)*v^2 # power from aircraft

All this adds up to:

F_T:=v->Vector(evalm(Fp/nu(v)^2*v+Fd*nu(v)*v+Fl*nu(v)*zip((x,y)->x*y,v([2,1]),Vector([-1,1]))+Vector(2,1,[0,-m*g]))); # I have tried it and it works

 

so up til here I am good. It is this next part that I can't seam to get.

Write a routine which uses Euler's method to solve the equation of motion numerically for velocity v(t):

m*dv/dt=F_T(v)

Test the program by trying a plane with intitial velocity [v0,0] such that it maintains this speed when the engines power is P=P0

We have been given an Esolve we can use:

Esolve:=proc(f::procedure,h,x0,y0,N::integer) # Calculates y(x0+n*h) for n=1..N given y0=y(x0) and f(x,y)

local n,y,x;

y[0]:=y0; # Start Value
x:=x0;

for n from 1 to N do
y[n]:= y[n-1]+h*f(y[n-1],x); # Euler's formula
x:=x+h; # Next x
end do;

y;

end proc;

 

If anyone could help me understand how it works and how to get this to work with vectors I would be very gratefull.

Vahid Borji

How can I plot the p stability region in H1and H2 region I already gotten the polynomial 

Hi every body.

I want to solve a differential equation:

ode=D(r(θ),θ).....

I have the initial conditions:

e=10^(-20)

r(e)=A where A is parameter.
r'(e)=0

sol:=dsolve({ode,r(e)=A,D(r)(e)=0},parameter=[A],numeric)

and:

All in the file.

#@#

Ode-Problem.mw

hi .please see attached file below and help me

thanks..indices(res_nolist).mw

Not homework (from the telly): A gallery takes a concave polygon shape with a square pillar in the centre. security cameras can do a 360 degree sweep but they can't see around corners. The cameras have to be attached to the walls. What is the fewest number of cameras such that they can see everywhere in the gallery?

I got as far as drawing it in Maple.

polygon_cameras.mw

there is an algorithm -which supposedly finds the optimal solutuion- breaking the object into triangular shapes. that gets an answer:  4 cameras.

EDIT 11/10

this is based on Fisk's short proof. See Markiyan's wiki ref below.

1.first stand on on a corner and scan clockwise around the room. Any two corners passed creates one triangle.

Repeat for every corner

 

2. Pick three colours and allocate each color to each corner of each triangle.

sometimes you will end up with a triangle which has 2 corners of the same colour. This one has two blue corners

 

This triangle must be broken in two and add a green dot

3.finally the algorithm places cameras on the colour which occurs least.

But by experimenting with more complex shapes (convex polygons) you can cover the gallery with 3.

 

In Maple anyone?

 

hi every one

please see attached file blew and help me for dsolve set equations.i dont know aboue errors with in

thanks

equation.mw

When solving ODE with dsolve, I don't want to use "_C1" as the name of constant, I want to specify by myself, how can I do?

Take for instance the signal [1,0,-3,2,1,0,1,2] (considered in Wavelets for Kids, Vidakivic & Mueler, AMS, 1991).

I want to anlalyse it down to the level zero with Haar wavelets. It seems that MAPLE's commnad only applies once.

 

 

 

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