Find the least number of moves and how many different ways that is achieved to win snakes and ladders with 1 die, with 2 dice, and how about 3 dice.  How to realize this with Maple?

Hello,

how do to inscribed cone in sphere ?

Thanks

Hi, i try the part of Real of the complex expression:

restart;
w := A*exp(-alfa(1+I)*y)+B*exp((1+i)*y);
            A exp(-alfa(1 + I) y) + B exp((1 + i) y)
u := Re(w);
          Re(A exp(-alfa(1 + I) y) + B exp((1 + i) y))

But does not work.

Regards.

This question explores the family of differential equations dy/dx=sqrt(􏰐 1 +􏰏( a*x )+ 􏰏 (2 *y)) for various values of the parameter a.  

For the case a = 􏰐 0 find the analytical solution that passes through the point (0, 1) and verify that this is a solution to the differential equation. Use this solution to find the value of y correct to 4 decimal placeswhen x=􏰐1. 

In maple i did

y:=(1/2)*x^2+sqrt(3)*x+1:
diff(y,x)
                             
i got the answer x + sqrt(3)

as shown in the markscheme. please cluld anyone help how to get y before this step and what to do after.

I have trouble solving this equation

fsolve(5000 = int(1/(0.1060444429e-1-0.2120888857e-1*X+0.1033933318e-1*X^2), X = 0 .. x), x)

It has a few points where the solution will go towards infinite, but that is not something that is an issue normally. I have no problems what so ever to solve this using my trusty TI-89, so Im wondering what needs to be done to actually solve this. I have tried giving an initial guess, and I have tried using solve, but it doesnt seem to do the trick.

Regards

Hi,

I need your help to classify the follwing set {0}, {1} and [0,1] are local attractor or not and in the case of local attractor how can we determine the bassin of attraction. 

ode:=diff(x(t),t)=sqrt(x(t));

how can we prove using maple which of {0}, {1} and [0,1] are local attarctor or not.

Many thanks

I have many linear equations as below(f,g,h,...,p, are linear of S,T,..,W):

y1=f(S[i,j],T[i,j],U[i,j],V[i,j],W[i,j]);

y2=g(S[i,j],T[i,j],U[i,j],V[i,j],W[i,j]);

y3=h(S[i,j],T[i,j],U[i,j],V[i,j],W[i,j]);

.

.

.

yn=p(S[i,j],T[i,j],U[i,j],V[i,j],W[i,j]);

Where (i,j)=(0,0),...,(I,J)

How ask Maple to write them in Matrix form as below:

AX=0

Where X is: X=Transpose{S[0,0],S[0,1],S[0,J],...,S[1,0],S[1,1],...,S[1,J],...,S[I,0],S[I,1],...,S[I,J],

                        T[0,0],T[0,1],T[0,J],...,T[1,0],T[1,1],...,T[1,J],...,T[I,0],T[I,1],...,T[I,J],...,W[I,J]}

Dear All,

I would like to plot the probability density function of a state variable obtained from solving differential equations. I have found that there are functions called "PDF" and "KernelDensityPlot" in the Statistics package, but they really confuse me. Could you please point me out? My code is as follows.

Ps. Is it possible to plot the PDF directly from the solution of dsolve() without discretizing the results? 

restart:
with(plots): with(DEtools): with(plottools):with(LinearAlgebra): with(Statistics):

v1:=1: f:=-4: v2:=2.515: omega:=1: epsilon:=0.001: k:=0:
sys:=diff(u1(t),t)=v1*u1(t)-(omega+k*u2(t)^2)*u2(t)-(u1(t)^2+u2(t)^2+3*z(t)^2)*u1(t),
     diff(u2(t),t)=(omega+k*u1(t)^2)*u1(t)+v1*u2(t)-(u1(t)^2+u2(t)^2+3*z(t)^2)*u2(t),
     diff(z(t),t)=z(t)*(-v1+3*u1(t)^2+3*u2(t)^2+z(t)^2)+epsilon*z(t)*(v2+f*z(t)^4):

t_start:=50: t_end:=300: dt:=0.05: fs:=1/dt:

solA:=dsolve({sys, u1(0)=0.6, u2(0)=0.6, z(0)=0.1},
             {u1(t),u2(t),z(t)},
              type=numeric, method=rkf45, maxfun=0,
              output=Array([seq(i,i=t_start..t_end, dt)])):

u1:=solA[2,1][..,2]:
u2:=solA[2,1][..,3]:
z:=solA[2,1][..,4]:

u0:=sqrt~(u1^~2+u2^~2+z^~2):

Phi:=z/~u0:

# How could I plot the probability density of Phi (y-axis) against Phi(x-axis)?

Probability_density_function_plot.mw

Thank you!

Very kind wishes,

Wang Zhe

How do I?
I'm very new in Maple, just I wanna learn a lot but i don't know where to start.
I have to find x,y, Tl, Th and Ti

Maybe we can help me at least a litle bit :D
thanks

I have $ signs suddenly apearing down the side of my document. They are randomly formatting numbers. Don't know how I turned it on. How to undo?  Do they affect calculation accuracy or are they purely dislap formatting

I'm new using maple and I trying to solve this equation:

u*(diff(u*(diff(R(u), u)), u))-(-m^2+u^2+fu)*R(u) = 0

Maple give this solution:

R(u) = _C1*BesselI(sqrt(-m^2+fu), u)+_C2*BesselK(sqrt(-m^2+fu), u)

But I don't know how I can find de constant C1 and C2.

Thanks in advance.

I have an equation were build with many unfixed numbers of variables as below:

eq:=f(U[i,j],V[i,j],W[i,j],S[i,j],T[i,j]), i,j=0,1,2,...(changing during the program running)

How do you suggest to calculate the first derivative of such equation with respect to U[i,j],V[i,j],W[i,j],S[i,j],T[i,j]?

Suppose that i,j=22, in this way to calculate the metioned derivative with respect to U[0,0] only, I must write:

diff( eq(U[0,0],U[0,1],U[0,2],...U[22,22], V[0,0],V[0,1],...,T[22,22]), U[0,0])  ( More than 2420 terms)

As you see it needs cumbersome writings if i,j be constants, and because the i and j are changing during the program, I dont know how to cope with this derivatives in Maple??

Here's a little procedure to fish out data from the Simbad database.  Some star names may not work if the page Simbad brings up is not completely filled, but it should work for most queries.

Download star_database_-_simbad.mw

What is the total number of the characters in "Vanity Fair" by William Thackeray?
How to determine it with Maple, making use of StringTools and EssayTools? I think an electronic version of this novel is free. 
AFAIK, there are about 600 personages in "And Quiet Flows the Don" by Mikhail Sholokhov.

PS. It happened to me to collaborate with Dr. I. Kulchytskyi on text analysis, but the asked problem is new for me.

PPS. Here is a link to the plain text.

Import("http://www.gutenberg.org/cache/epub/599/pg599.txt");

I found this http://www.atlasoftheuniverse.com/50lys.html and wondered how to do it in Maple. With a bit of data file editing I came up with this.  All stars within 50 light years that are visible to the naked eye.

The modified data file and the maple worksheet below

stars3.txt

Download Stars50LY.mw