Hi,

I have an ode like this

ODE:=(diff(T(x), x, x))+P*(S+a*(1-exp(-L*x))/L)*(diff(T(x), x))=0;

bcs:=T(0)=1,T(infinit)=0;

where P, S, L a, are all constants.

let assume that 

z=P/L^2*exp(-L*x);

subing z into the ode, we can have

ode1:=diff(T(z), z$2)+(1+z*a-P)*(diff(T(z), z)) = 0;

bcs1:=T(P/L^2)=1,T(0)=0;

Is it possible to find a closed form solution (T(x) in a compact form)?

I'm trying to display some flow lines for a vector field. The vector field I have is:

What I put into Maple is:

I've tried this with a number of points, but I always get an error message along the lines of:

"Error, (in Student:-VectorCalculus:-FlowLine) cannot determine if this expression is true or false: (2.*(1)(0)-4.)^2+(-2.+4.*(1)(0))^2 < 0.9e-9"

Could someone please shed some light as to what's going wrong for me? I would be very grateful for any help.

Thanks.

For the recursive equation

x_n − 10x_n−1 + 50x_n−2 = 0
n = 2, 3, ...
x₀ = 0
x₁ = 10

How do I calculate x_n in Maple? I'm wondering because n doesn't start at 0 but at 2, how will that make a difference?

Thanks in advance!

Hi, the display function in the simplex package gives us a nice breakdown of the form Ax<=b, but how do we extract the individual elements, i.e. the matrix A and vectors x and b? Normal indexing into the expression doesn't work, i.e. if for some set of constraints of the form 2x+3y<=21 we enter

res:=display(constraintSet);

this gives us a nice expression, but res[1] etc. doesn't work as we might hope (i.e. by returning the matrix A).

a := matrix(...);
b := Convert to hermit matrix from a;
Norm(MatrixMatrixMultiply(b, a), 2) = Norm(a,2)^2

i have tried, but not exactly equal
Norm(MatrixMatrixMultiply(b, a), 2) = 0.01
Norm(a,2)^2 = 0.1

Guess what matrix a is?

How to calculate colimit with only substitution and solve? Any simple example to show the steps.

run a command string in C# by calling maple

it can run in maple if copy into maple

however return input string was not in correct format

String commandstring = "restart;with(LinearAlgebra):with(ExcelTools): filename := "0257.HK";open3 := Import(cat(cat("C://Temp//HK//Transportation//",filename),".xls"), filename, "B2:B100");high3 := Import(cat(cat("C://Temp//HK//Transportation//",filename),".xls"), filename, "C2:C100");low3 := Import(cat(cat("C://Temp//HK//Transportation//",filename),".xls"), filename, "D2:D100");close3 := Import(cat(cat("C://Temp//HK//Transportation//",filename),".xls"), filename, "E2:E100");n := 30;Round := proc(x,n::integer:=1) parse~(sprintf~(cat("%.",n,"f"),x)); end proc: t:=1; gg :=Matrix(n+1,1); ggg :=Matrix(n+1,1); for k from 0 to n do InputMatrix3 := Matrix([[close3[t+1+k] , close3[t+k], close3[t+2+k]],[close3[t+k], close3[t+2+k],0],[close3[t+2+k],0 , 0]]): InputMatrix3b := Matrix([[close3[t+2+k], close3[t+1+k] , close3[t+3+k]],[close3[t+1+k] , close3[t+3+k],0],[close3[t+3+k],0 , 0]]): InputMatrix3c := Matrix([[close3[t+3+k] , close3[t+2+k], close3[t+4+k]],[close3[t+2+k], close3[t+4+k],0],[close3[t+4+k],0 , 0]]): Old_Asso_eigenvector := Eigenvectors(MatrixMatrixMultiply(Transpose(InputMatrix3), InputMatrix3)): Old_Asso_eigenvector2 := Eigenvectors(MatrixMatrixMultiply(Transpose(InputMatrix3b), InputMatrix3b)): Old_Asso_eigenvector3 := Eigenvectors(MatrixMatrixMultiply(Transpose(InputMatrix3c), InputMatrix3c)): gg[k+1,1] :=Old_Asso_eigenvector[2][1,1]; od;Round(Re(gg[1,1][1,1]));";

alpha:= (1/2)*(-y*t2-x*t1-y*t3+sqrt(y^2*t2^2+2*y*t2*x*t1+2*y^2*t2*t3+x^2*t1^2+2*x*t1*y*t3+y^2*t3^2-4*x*t4*y*t9-4*x*t4*y*t8-4*x^2*t4*t7-4*y^2*t5*t9-4*y^2*t5*t8-4*y*t5*x*t7-4*y^2*t6*t9-4*y^2*t6*t8-4*y*t6*x*t7))/(x*t4+y*t5+y*t6);
g := -y/x;
f := (-x+sqrt(x^2-x*y-2*y^2))/(2*y+x);
subs(p=f,subs(q=f,subs(x=p,subs(y=q,g))));
g := (1/2)*(-x+sqrt(x^2-4*y*x-4*y^2))/(x+y);
f := x*y;
gof := subs(p=f,subs(q=f,subs(x=p,subs(y=q,g))));
lhsgofoalpha := subs(q= alpha,subs(p=alpha, subs(x=p,subs(y=q,gof))));
foalpha := subs(p= alpha,subs(q=alpha,subs(x=p,subs(y=q,f))));
rhsgofoalpha := subs(x= foalpha,subs(y= foalpha, g));
osys := lhsgofoalpha = rhsgofoalpha;
sys1 := subs(x=0, osys);
sys2 := subs(y=0, osys);
sys3 := subs(x=1, osys);
sys4 := subs(y=1, osys);
sys5 := subs(x=2, osys);
sys6 := subs(y=2, osys);
sys7 := subs(x=3, osys);
sys8 := subs(y=3, osys);
sys9 := subs(x=4, osys);
sys1 := subs(x=3,subs(y=2, osys));
sys2 := subs(x=5,subs(y=1, osys));
sys3 := subs(x=1,subs(y=5, osys));
sys4 := subs(x=1,subs(y=2, osys));
sys5 := subs(x=2,subs(y=5, osys));
sys6 := subs(x=5,subs(y=2, osys));
sys7 := subs(x=2,subs(y=1, osys));
sys8 := subs(x=3,subs(y=5, osys));
sys9 := subs(x=5,subs(y=3, osys));
res:=solve([sys1, sys2, sys3, sys4, sys5, sys6, sys7, sys8, sys9], {t1,t2,t3,t4,t5,t6,t7,t8,t9});
eval(osys,res);
simplify(%);
`~`[lhs](select(evalb, res));

(g o f ) o alpha =g o (f o alpha)
restart;alpha := (1/2)*(-x-x*t1-y*t2-y*t3+sqrt(x^2+2*x^2*t1+2*x*y*t2+2*x*y*t3+x^2*t1^2+2*x*t1*y*t2+2*x*t1*y*t3+y^2*t2^2+2*y^2*t2*t3+y^2*t3^2-4*x*t4*y*t9-4*x^2*t4*t7-4*x*t4*y*t8-4*y^2*t9-4*y*x*t7-4*y^2*t8-4*y^2*t5*t9-4*y*t5*x*t7-4*y^2*t5*t8-4*y^2*t6*t9-4*y*t6*x*t7-4*y^2*t6*t8))/(x*t4+y+y*t5+y*t6);
g := -y/x;
f := (-x+sqrt(x^2-x*y-2*y^2))/(2*y+x);
subs(p=f,subs(q=f,subs(x=p,subs(y=q,g)))); # -1
g := (-x+sqrt(x^2-x*y-2*y^2))/(2*y+x);
f := x*y;
gof := subs(p=f,subs(q=f,subs(x=p,subs(y=q,g)))); # -(1/3)*(y/x+sqrt(-2*y^2/x^2))*x/y
lhsgofoalpha := subs(q= alpha,subs(p=alpha, subs(x=p,subs(y=q,gof))));
foalpha := subs(p= alpha,subs(q=alpha,subs(x=p,subs(y=q,f))));
rhsgofoalpha := subs(x= foalpha,subs(y= foalpha, g));
osys := lhsgofoalpha = rhsgofoalpha;
sys1 := subs(x=0, osys);
sys2 := subs(y=0, osys);
sys3 := subs(x=1, osys);
sys4 := subs(y=1, osys);
sys5 := subs(x=2, osys);
sys6 := subs(y=2, osys);
sys7 := subs(x=3, osys);
sys8 := subs(y=3, osys);
sys9 := subs(x=4, osys);
sys1 := subs(x=3,subs(y=2, osys));
sys2 := subs(x=5,subs(y=1, osys));
sys3 := subs(x=1,subs(y=5, osys));
sys4 := subs(x=1,subs(y=2, osys));
sys5 := subs(x=2,subs(y=5, osys));
sys6 := subs(x=5,subs(y=2, osys));
sys7 := subs(x=2,subs(y=1, osys));
sys8 := subs(x=3,subs(y=5, osys));
sys9 := subs(x=5,subs(y=3, osys));
res:=solve([sys1, sys2, sys3, sys4, sys5, sys6, sys7, sys8, sys9], {t1,t2,t3,t4,t5,t6,t7,t8,t9});
eval(osys,res);
simplify(%);
`~`[lhs](select(evalb, res));

I want to begin by saying hello! im new to the forums i hope some one can give me a push in the right direction with some of my maple homework. im sort of stuck on a few of these questions and would be greatfull for some help. 

Let .

a) Let g be the tangent line to f when x = c. Use Maple to find g as a function of c.

b) Use Maple to plot f and g(3) using view = [0..5, -25..100].

c) Define a function called plot_tan that plots both f and g(c) where f is blue and g(c) is red. Also use the same view as in part (b). Note that plot_tan is also a function of c.

d) Using your function plot_tan, the following all in one graph using the display command:

plot_tan(1), plot_tan(1.5), plot_tan(2), plot_tan(2.5), plot_tan(3), plot_tan(3.5), plot_tan(4), plot_tan(4.5), plot_tan(5).

e) Try using the option insequence = true in the display command. What does this option do? (You will need to click on the graph and play around with some buttons).

now it seems to me i have to use the point slope formula to get to a fuction g of c. thanks in advance! i hope you can help

Hello!

I am trying to create a Fortran routine that creates and populates a large 2D array, using Maple's codegen or CodeGeneration capabilities. I would like Maple to create the Fortran code so that the column-major ordering is respected: I would like Maple to populate mat(1,1), mat(2,1), mat(n,1) before moving on to mat(1,2)... Unfortunately, codegen and CodeGeneration seem to only produce row-major code.

Any idea on how to proceed, or an option of the code generation that I would have missed?

Thanks for your help!

Etienne

soslve('(cosh(C + cosh(C))/cosh(C) = 2') gives me a "Waning, solutions may have ben lost" message and no answer.

Write a procedure which inverts a given 2x2 matrix ie
Given a list of 4 numbers (a,b,c,d) return numbers (x,yz,w) such that
Matrix(a,b,c,d)(Matrix(x,y,z,w)) =Identity matrix

I want to find the area of the triangle ABC with the sides are a, b, c. I tried

a:=sqrt(91)/6:

b:=sqrt(17)/2:

c:=sqrt(13)/3:

p:=(a+b+c)/2:

s:=simplify(sqrt(p*(p-a)*(p-b)*(p-c)));

How can I get the result sqrt(523)/24?

How to test  associativity?

How to determine which of below has associativity?

The definition x*(y*z) = (x*y)*z.

asso := -(1/2)*(x+y+sqrt(x^2+2*x*y-3*y^2))/y;
asso := -(1/4)*(2*x+y+sqrt(4*x^2+4*x*y-7*y^2))/y;
asso := -(2*x+y)/(y+z);
asso := (1/2)*(-y-z+sqrt(y^2-2*z*y+z^2-8*z*x))/z;
asso := (1/2)*(-z+sqrt(z^2-4*z*x-4*z*y))/z;