## Integration of Planck radiation law...

I'm trying to obtain integral of Planck radiation law in Maple:

with this command:

```f := (2*h*(c)^(2))/((x)^(5))*(1)/(exp((h*c)/(x*k*T))-1);
int(f,x=0..infinity);```

but I get some terrible limit that cannot be solved instead of the correct result:

How to obtain correct integral?

planck.mw

## boundary conditions...

the program shows that the error please verify it sirprogram11.mw

## problem with PDE ...

what's the problem with PDE below? tnx for help

 > restart:
 > PDE:=diff(u(x,t),t)=k*diff(u(x,t),x\$2)-h*u(x,t);
 (1)
 > IBC := {u(-Pi,t)=u(Pi,t), (D[1](u))(-Pi, t) = (D[1](u))(Pi, t),u(x,0)=sin(x)};
 (2)
 > pdsolve(PDE,IBC);
 >

## Solving and optimizing problem...

Hi

I have two equations as follows:

The goal is finding the parameter 'phi'. This parameter is a positive real numeric constant.

I uploaded two files that they are included two methods to solve the problem.

1.mw

2.mw

Is method in the first file mathematically logical? If it is a correct method, why the command fsolve dosent work?

In file 2, we have 2 equations with further indeterminantes. The constant 'phi' must be minimum possible amount. How we can use the commands like the Minimize in Optimization? Please hint me.

Thank you very much

## Insering Legend inside the figure plot ...

I want to set the position of the legend inside the figure window for example say top right in the figure window. Maple chose the legend to be at right, left, top, bottom outside the figure window. How can I place the legend of my own wish?

thanks,

## Maple cause error but doesn't show the reason...

I am coding a big module to solving my project : analyze function in math, but when I compile my module maple return "Error," but it doesn't tell me what error happened.

I check the maple help and it said:" If no msgString is given, error raises the most recently occurring exception" but I have no exception before.

This is the pic of that error.

## Can I plot3d with an condition?...

I would like to look at a 3d plot including an condition about the tree variables of the plot

For this simple case, I only want to see the plot with the condition that
{40 < y, x < y-40, z < y-40} or {x = 0, y = 40, z <= 0}, {y = x+40, 0 < x, z < x}, {y = x+40, z = x, 0 < x}

. Is that possible?

In 2d there is no problem. And in 3d I do not know how.

## how do i get rid out of error for ploting hardenin...

restart; with(plots, implicitplot);
print(`output redirected...`); # input placeholder
[implicitplot]
p; .2; omega[0] := 1; epsilon[1] := 1.04493; epsilon[2] := .93259; delta := 0.2e-1;
eq := [[omega[0]*a-a*Omega^2+(3/4)*epsilon[2]*a^3]^2+(delta*Omega*a)^2 = p^2];
print(`output redirected...`); # input placeholder
implicitplot(eq, omega = .5 .. 2, a = 0 .. 5, p = 0 .. 1, color = blue, thickness = 2, gridrefin = 6);
%;
Error, (in plots/implicitplot) invalid input: the following extra unknowns were found in the input expression: {Omega, p}

## Transformation of Random Variables - How to?...

Hello

I am exploring the Statistics package to see how Maple implements the transformation of random variables.  Unfortunately, I got stuck when trying the following example.

W->X+Y and then X-> W/2

For the first part, I did

but for the second part I could not figure out what to do.

Any suggestions?

Many thanks

Ed

## How to get the value of an environment variable ?...

Hi everybody,

I'm working under Windows 7

My need :
A MAPLE code has to be run from an ECLIPSE session (through a cmaple MyCode).
In this ECLIPSE session the user chooses a data file among many, and ECLIPSE then has to tell MyCode what file it has to read.

The solution I figured out :
Step 1 : ECLIPSE  set an environment variable "DataFile" which contains the user's choice, for instance set MyData=NameOfTheFile
Step 2 : Within MyCode I get the value of MyData from these two commands

MyFile := getenv(DataFile):

This doesn't work ( getenv(DataFile) returns [1," "] instead of the desired file name).
In fact it seems that getenv enables access to the “native” environment variables of Windows only (for instance HOMEDIR), not to the user defined environment variables (?)

Is  it possible to fix this and how ?

PS  : I face the same difficulties if I type set MyData=NameOfTheFile directly from a cmd command and try to access the value of MyData from a Maple session

## how to compute the most simplified result with sol...

solve(diff(-1/x,x) = (-1/x)^(b), b);

originally is 2, but it use ln(....) to express

if start from substitute, it seems need to replace manually.

solve(subs(a(x)=-1/x,diff(a(x),x) = (a(x))^(b)), b);

goal is to find b in equation below
solve(diff((x^2+x+1)/(-1+x)^2,x) = ((x^2+x+1)/(-1+x)^2)^(b), b);
(2*x+1)/(-1+x)^2-(2*(x^2+x+1))/(-1+x)^3 = ((x^2+x+1)/(-1+x)^2)^(b)

solve(diff((x^2+x+1)/(-1+x)^2,x) = ((x^2+x+1)/(-1+x)^2)*(b), b);

## How do I solve a set of differential equations in ...

Hi, my dear friend,

i am solving 9 ODE with boundary conditionsNigam.mw

 >
 (1)
 >
 (2)
 >
 (3)
 >
 (4)
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 (5)
 >
 (6)
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 (7)
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 (8)
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 (9)
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 (10)
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 (11)
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 (12)
 >
 (13)
 >
 (14)
 >
 >

Maple Worksheet - Error

then i got this error

Error, (in dsolve/numeric/bvp) initial Newton iteration is not converging

i dont know where i need to change.. could you help me..

## expand without simplify...

hi:

i'm using expand cmd, but surprisingly, not only execute the expand but execute simplify cmd. Is there any cmd only execute expand withoud simplify?

Best wishes,

from China

## How do I get a State Space representation from sys...

I've derived some system matrices from a equation which represents the dynamics of a mechanical system, I've searched for a way to convert this or represented in state space form but I can't figure out how to do it.

## issue with fsolve and Directsearch command in mapl...

Hi,

I have three simultaneous equations  with three unknown variables (E, W, T). When I solve these  simultaneous equations with fsolve command without specifying any range for variables, I don't get desirable root ( equation sol4 in maple worksheet- {E = 0.1007672475e-2, T = .7969434549, W = 0.1937272759e-2}). For this problem, I know the correct root {E = 2843.916504, T = .2782913990, W = 5344.844134} beforehand which maximize the objective function TP (equation sol8 in maple worksheet) and when I specify the narrow range of variables around the already known correct root in the fsolve command, then I get correct root ( equation sol5 in maple worksheet). If I don't know the actual answer (correct roots of the simultaneous equation) beforehand, How  could I get the correct root with fsolve command because it is very tedious work to specify different range in fsolve command repetitively to solve it by trial and error.

I also tried Direct Search method as suggested in this forum  but DirectSearch is also not able to provide the correct root (equation sol6 in maple worksheet). If I specify the narrow range around known root in direct search method ( equation sol6a in maple worksheet), then it would provide close to optimal root but if I don't know the correct root beforehand, then I couldn't specify the narrow range of variables, then how can I get correct root through direct search command.

Equation sol10 in maple worksheet  (objective function value at correct root) confirms that {E = 2843.916504, T = .2782913990, W = 5344.844134} is the correct root because it provide the value of objective function (TP) equal to 78285.85621 as opposed to negative value (TP value -12.53348074 in equation sol9)  produced by incorrect root  {E = 0.1007672475e-2, T = .7969434549, W = 0.1937272759e-2}).

Is there any method which would provide all the roots of these simultaneous equations which also include correct root. Maple worksheet is attached.

I am trying fsolve and direct search method with known root so that I could get the proper procedure to get the correct root which I can apply to another problem (set of similar simultaneous equations) for which I don't know correct root beforehand.