Hi everyone

When I solve these nonlinear ODEs, there is this problem i.e. Highlighted in yellow, in my solution. How can I solve it?

thanks a million!

nonlinear_ODE.mw

Hi, I have 2 Questions about programming in maple. I will be thankful if you help me as soon as possible.

First; How can I display a n*n HilbertMatrix?

Second: I wanna make a 2*2 matrix which its transpose is egual to its inverse, How can I do that by helping reflectionmatrix?

(I'm an amateur programmer, I use maple 13 on my pc)

a1:= f(x) :
> T1 :=simplify((taylor(a1,x=alpha,N+3))):
> E1:=subs([seq(((D@@i)(f))(alpha) = 0,i=1..m-1),f(alpha)=0,x=e[n]+alpha],T1):
> g1 :=(convert(simplify(series((E1,e[n]=0,N))),polynom));

Hi everyone...!

Can somebody tell me how to express this equation in Maple? 

x_ij <= z_kl ; ∀ i ∈ I: S(i)=k, ∀ j ∈ B: R(j)=l; 

Currently I'm dealing with containerization problem and have 4 indexes in the constraints (namely: i for item, j for container, k for shipment, l for route, S for Set of Shipment, and R for Set of Route) while x and z are binary variables. What I want to express is: (for example), item 1,2,3 are in shipment 1, item 4,5 are in shipment 2, etc etc. SO, if i = 1,2,3 then the value of k will be 1. If i = 4,5 then the value of k will be 2, etc. Same thing goes to j and l, (for example) if j = 1,2 then the value of l will be 1, etc etc. Further depcition is more or less like this:

S(i) = k

S(1) = 1

S(2) = 1

S(3) = 1

S(4) = 2

S(5) = 2

Thank you very much for the help.

HI, I am trying to solve two PDEs but in boundry conditions there is arising an error plz help.
Nazi.mw

To check one of the MythBusters TV episodes, i.e., the fall of a mannequin (80 Kg) from a plane at an altitude of 1200 m in 31 s, with Maple13 (Windows Vista) I solved the following differential equation with initial conditions:

> de:= m*(D@@2)(x)(t) = m*g - k*(D(x)(t))^2:

> ini:= (x(0) = 0, D(x)(0) = 0):


> X:= unapply(rhs(expand(dsolve({de,ini}))),t);

        X := proc (t) options operator, arrow; -m^(1/2)*g^(1/2)*t/k^(1/2)-m*ln(2)/k+m*ln(exp(2*g^(1/2)*k^(1/2)*t/m^(1/2))+1)/k end proc

1) Posing: V0 = sqrt(m * g / k),  T = sqrt(m/(g*k)) one has  V0*T = m/k. I want to have:

   > Xxb:= t -> V0*(- t + T * ln((exp(2*t/T) + 1)/2) ); # m.

 How to obtain this equivalent equation  Xxb(t), without retyping the equation of  X(t) ? With subs , convert or simplify  applied to  X(t), Maple 13 gives error messages.

2) Taking the derivative of  Xxb(t), one find :

     V := proc (t) options operator, arrow; V0*(exp(2*t/T)-1)/(exp(2*t/T)+1) end proc.

How to transform it to V = V0 tanh(t/T) ?

Again, subs , convert or simplify  seem not working, even with  assume(t, real), assume(T, real) ! I know simplify is a difficult task, but Maple should recognize a tanh !

Thank you in advance for any suggestion.

( Note that with m = 80 Kg, g = 9.81 m/s^2 and k = 0.267482 Kg/m, which correspond to a speed limit of V0 =195 km/h, on find t(1200m) = 26 s, instead of 31 s ).

let γ be the root 

i have to apply taylor series on f(x) and then do some substitution like (helped by a member of Mapleprime)

restart;
taylor(f(x), x = gamma, 8);
f(x[n]) := subs([x-gamma = e[n], f(gamma) = 0, seq(((D@@k)(f))(gamma) = factorial(k)*c[k]*(D(f))(gamma), k = 1 .. 1000)], %)

then find the derivative of result from above output

i do

b := diff((x[n]), e[n])

basically i have to find the value of newton method which is

y_n=x_n-f(x_n)/D(f)(x_n)

here we substitute x_n=γ and D(f)(x_n)=b

and then want to apply f on y_n

there are to problem which i face 

1  f(x_n)/D(f)(x_n) is not in simplified form i-e O(e[n]^8) and O(e[n]^7) is appeared in numerator and denominator respectively. how we get the simplified result.

2 wht step should i do to find f(y_n)

plx help me to do this 

thanx in advance

i am new on maple while usig maple i have to substitute a general value in an equation but could not do it like

> restart;
> taylor(f(x), x = gamma);

i typed this and want to replace x-gamma with e[n] which is easy and i did it but whn i want to substitute D(f)(gamma),(D@@2)(f)(gamma) and so on by (D@@k)(f)(gamma)=k!*c[k]*f(gamma) then i could not understand how can i do 2nd part 
pls help in this i m very thanlful to you

Dear hope you will fine. I am try to make a program of square free factorization over a finite field whose alogrithm is below:

Algorithm: SFF (Square-Free Factorization)
  Input: A monic polynomial f in Fq[x]

Output: Square-free factorization of f

i←1; R ← 1; g ← f′;
  if g ≠ 0 then {
     c ← gcd(f, g);
     w ← f/c;
     while w ≠ 1 do {
           y ← gcd(w, c); z ← w/y;
           R ← R·zi; i ← i+1; 

           w ← y; c ← c/y }
     if c ≠ 1 then {
           c ← c1/p;

           Output(R·SFF(c)p) }

     else  Output(R)
  else {
           f ← f1/p;

           Output(SFF(f)p) }

  end.

The attached file my try to make this, please find and help me to complete this. I am waiting your kind response.

Help.mw

With my best regards and sincerely.

Dear

Hope everything going fine with you. I have question

f := x^11+2*x^9+2*x^8+x^6+x^5+2*x^3+2*x^2+1

g := 2*x^10+x^7+2*x^4+x

if we take gcd of infinite field its answer is x^6+1 

and the GCD(3)[x]=Z_3[x] is given by x^9+2x^6+x^3+2

How we find GCD(3)[x] in maple. 

With my best regards and sincerely.

EF.3.mwHi, I want to ask that how to find the exact solution of equation without applying any technique

Hello 

I have maple 13, and I installed two new packages, the problem that I don't know where should I saved them and how to make them active to start using there routines ??? 

So pleas any one know how to add packages to maple 13, help me    :) 

Hi there

I use Maple13 for plotting the surface of revolution of y=x^2 around the line y=1 on the interval [1,2]. But the distance between the surface 

and the vertical axis is ignored while there must be 1 unit distance.please specify the correct command.

Thanks for your cooperation

Regards

M. R. Yegan

I have the following code of a plot:

plot(
[
add(BS(bb[4], t, i, 3)*bb[1](i+1), i = 0..n),
add(BS(bb[4], t, i, 3)*bb[2](i+1), i = 0..n),
t = 0..1
],
color=red, axes=normal, scaling=constrained, numpoints=100, thickness=2
):

and I get the following error:

Error, (in BS) cannot determine if this expression is true or false: 0 <= t and t < .54901960784313725490196078431373

The problem is that, in the definition of BS, there are some conditions that depend on the variable t. It seems that Maple does not use a specific value of t when executing BS. My solution is to plot specific points, i.e., 

plot(
[
seq([add(BS(bb[4], h/5000, i, 3)*bb[1](i+1), i = 0..n),
add(BS(bb[4], h/5000, i, 3)*bb[2](i+1), i = 0..n)], h=0..5000)
],
color=red, axes=normal, scaling=constrained, numpoints=100, thickness=2
):

Can this be done in a more elegant way?

HPM_4.mwhi, I am using homotopy perturbation technique but there is arising an error in comaring coeffecient of p^0, p^1,.... plz help me