## How to find area of the region bounded by the give...

How can I found the area of the region bounded by

y=e^xcos(x), y=o, x=−π/2, x= π/2 ?

## doublefactorial weirdness...

I have an example where I try to calculate an infinite sum (G&R1.641.1)  in Maple 2022 (or 2021).  I get a different numerical result when I evaluate the sum if I express the coefficients c(m) in the sum using Maple's doublefactorial function for m!! (c1(m)) or the equivalent expression involving the factorial function (c2(m)).  Only the latter gives the correct value for the sum.  This happens even though Maple gives the same numerical value for the coefficients c1(m) and c2(m).  What's going on?? Please see the attached spreadsheet.

## Jacobi method solve linear system...

Dear all

I solved a linear system using Jacobi method , then I plot the solution, someting is wrong, I can't plot the solution

jacobi.mw

## How to factor out a number...

I have the following expression (result of a calculation):

`(1/1296)*cBooP0-(1/1296)*cSRP0-(1/1296)*tStartRamp*f__SR/N`

Rather obviously the common factor 1/1296 can be factored out, except I cannot get Maple to factor the 1/1296 without also factoring out N, which I do not want. My desired end result is this:

`(1/1296)*(cBooP0-cSRP0-tStartRamp*f__SR/N)`

I don't seem to be able to coerce Maple to do this. I can freeze the tStartRamp*f__SR/N term (leaving the 1/1296 unfrozen), but in that case I don't get Maple to pull the 1/1296 factor out at all.

Any hint would be appreciated. I am doing this on Maple 2015. It is really a bit cosmetic, but sometimes I use Maple to write "smart" documentation & then I'd like to end up with a somewhat polished result.

Mac Dude

## How do I modify the code for initial value problem...

Dear all,

Please I want to solve the following boundary value problem numerically with the attached code

y''=((y')^2+y^2)/(2*exp(x)),      0<x<1

with boundary conditions as follows

y(0)-y'(0)=0, y(1)+y'(1)=2*exp(1)

The exact solution is y(x)=exp(x).

How do I modify the code to be able to handle it?

Please the delta in the code represents y'.

Thank you for your time and best regards

restart;
 >
e1:=y[n+2] = (1/12)*h^2*f(n)+(5/6)*h^2*f(n+1)+(1/12)*h^2*f(n+2)+2*y[n+1]-y[n]:
 >
 >
 >

h          Num.y          Num.z            Ex.y           Ex.z        Error y        Error z
0.25000      0.702642933  -11.119327426    0.044732488   -9.516563326       0.65791         1.6028
0.50000     -1.480941776    3.706008390   -0.195836551   -1.080050970        1.2851         4.7861
0.75000      2.177304037    3.857405154    1.966274055   -2.618345553       0.21103         6.4758
1.00000     -0.353401232  -12.899134092   -0.541621655  -16.265122833       0.18822          3.366
1.25000      2.205257809   -0.748313267    1.880461001    0.803458961        0.3248         1.5518
1.50000     -0.457853582   -9.260175135    0.888094914  -17.501091793        1.3459         8.2409
1.75000      2.368665639   -0.220734441    0.227799905   -7.823705892        2.1409          7.603
2.00000     -0.556459764  -11.300336415    2.230324739   -5.428300487        2.7868          5.872
2.25000      2.205494666   -0.953807966   -0.582405956  -17.141951993        2.7879         16.188
2.50000     -0.947043873  -11.871777444    1.457323206    3.126163062        2.4044         14.998
2.75000      1.867780693   -1.104185167    0.366014055  -11.889781987        1.5018         10.786
3.00000     -1.448466064  -12.600325627   -0.692660166   -0.858678078       0.75581         11.742
3.25000      1.408438927   -1.076955833    1.243407129    4.765140072       0.16503         5.8421
3.50000     -1.960671678  -12.838644035   -1.682658102   -6.465546461       0.27801         6.3731
3.75000      0.947838606   -0.761420206    0.210882522   14.697480238       0.73696         15.459
4.00000     -2.352223093  -12.652936159   -0.678627396    0.245000716        1.6736         12.898
4.25000      0.596650899   -0.266003839   -1.802692162    9.387643085        2.3993         9.6536
4.50000     -2.528856863  -12.055589881    0.398695396   14.817725265        2.9276         26.873
4.75000      0.441416507    0.296276900   -2.296698552    0.729525901        2.7381        0.43325
5.00000     -2.446901406  -11.201642111   -0.256333100   19.522565217        2.1906         30.724

 >

## Analyzing large instance problem using LPSolve pac...

As the LPsolve package returns the solution points in a list format, how we can analyze the list if we're having a large instance problem? By large instance, I mean that there are around 1500+ variables in the linear programming model.

Also, I have attached the screenshot of the output in this thread. To perform further analysis, I want to fetch the value of the DQV, QF, and UQT variables. But since the list contains the values as an expression, for example DQV[0, 0, 0, 0] = 0. In such cases, I cannot perform mathematical operations for the solution points results.

Also, if I can delete the DQV[0,0,0,0] from the expression mentioned above, I'll end with the numeric values list, which can then be converted into an array and make things easier for me. But currently, I'm struggling to delete the DQV part of the expression in one go (manually deletion for each expression, it's very time consuming to delete for 1500 variables).

Please suggest to me some approach to deal with this issue.

I am thanking you.

Regards

## Problem-With-Boundary-Condition-At-Infinity...

I am having a problem in evaluating a fluid flow problem at a boundary that includes infinity using a semi-analytic method Adomian Decomposition Method.

Find the attached code. Thanks in advance.

## How do I export a DataFrame as latex code? |Bug re...

I recently upgraded to Maple 2022 just to use the new `latex` command. It seems I still can't export `DataFrame` types, I'm very disappointed. What am I doing wrong?

```restart:
test:= DataFrame( [[1]], columns = [1] );
latex(test);
```

returns:

`Error, (in DataFrame:-type) invalid input: subtype expects its 2nd argument, _t, to be of type type, but received And(symbol,satisfies(u -> substring(u,1 .. 9) = ('`\\mapleref`')))`

Using `File > Export As > LaTeX` also doesn't work.
Printing the function call using ` printlevel := 100000:` returns the following:

I've attached the worksheet for reference. Demo.mw
Does anyone know a workaround?

-Thanks for the Help

## table of results using columns ...

dear all

I try to create a table with four columns but someting wrong, the code contains few lines,

table_columns.mw

## Error, (in fsolve) number of equations, 4, does no...

dear all

I have a system of 4 equations with 4 unkowns, but maple says that there 7 unknowns, and fsolve does return any solution

problem_solve_system.mw

Thanks

## Vector spaces from sets...

Hi! I'm new to Maplesoft. I would like to use it for my research. However, in order to do so, i have to construct an n-dimensional vector space, with vectors of the form A_1*B, A_2*B, ..., A_k*B, where A_i is a set of  n components from a Field (or ring) and B is the basis for the vector space.

It would REALLY help if you could give some ideas for me to bring this up, or else i will be forced to typset every one of the vectors i'll use in a matrix-multiplication form and will make considerably harder my work.

## loop over table...

Just wondering how I do a loop over the contents of the table. I need both the index variable and the stored value associated with it.

This one apparently doesn't work.

 (1)

 (2)

 (3)

 (4)

## simplifying complex expressions...

How do I simplify :

```Zin := Rin + omega*L*I + (omega*L)^2/(RL + omega*L*I);

```

so that there are no imaginary terms in the denominator?

I've tried,

```assum := Rin::real, omega::real, L::real, RL::real, 0 < Rin, 0 < omega, 0 < RL, 0 < L
Zin := Rin + omega*L*I + (omega*L)^2/(RL + omega*L*I);

(simplify(Zin) assuming assum);
```

but this doesn't work.

## dsolve ode with Bcs...

Dear all

I tried to solve a second order ODE, using dsolve but maple doest not return an explicit solution and no solution plotted.

solve_ode.mw

Hey everyone,

I am trying to solve this differential equation for h(u):

h(u)^2 + 2*a*h(u)/sqrt(1 + diff(h(u), u)^2) = b^2

for given values of a and b. For a=3 and b=1 maple gives :
u - Intat((_a + 1)*(_a - 1)/sqrt(-(_a^2 + 6*_a - 1)*(_a^2 - 6*_a - 1)), _a = h(u)) - _C1 = 0, u - Intat(-(_a + 1)*(_a - 1)/sqrt(-(_a^2 + 6*_a - 1)*(_a^2 - 6*_a - 1)), _a = h(u)) - _C1 = 0

and I dont know what to do from there. Any help would be very much appreciated

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