## limits of Boundary Data...

I cannot remember that this was an issue in Maple 6/9/11, so it must have changed later on up to 22.

The following limit fails to execute

restart;
1/(r_S^5*(_C2*r_S^4 + _C2*r_S^3 + _C2*r_S^2 + f[3](0)*r_S + f[4](0)));
limit(%, f[4](0) = infinity);

It fails to calculate the limit with result as zero.

Thanks

## Using an numeric integral for a numeric pdsolve...

I want to solve a pde numerically, where one of the initial conditions involves an integral expression. In essence, I would like to get the following code to run.

```restart;
with(PDEtools);

# the heat equation
pde := diff(v(x, t), t) = diff(v(x, t), x, x);

f := x -> exp(-x^2);

a := -1.68858; b := 1.68858; delx := 1/100; t_final := 5;

pds := pdsolve(pde, {v(a, t) = 0, v(b, t) = 0, v(x, 0) = 1 - int(f(f(s)), s = 0 .. x)}, numeric, range = a .. b, time = t, spacestep = delx);

Error, (in pdsolve/numeric/process_IBCs) improper specification of initial/boundary condition: additional unknown(s) {s} were found in v(x,0) = 1-int(exp(-exp(-s^2)^2),s = 0 .. x)

pds:-animate(frames = 120, t = t_final);```

Maple doesn't have any built-in function to evaluate the integral expression, so the initial condition doesn't evaluate to a simple expression involving x. I hope that because pdsolve is outputting numerical results, it should be acceptable for the initial condition to output floats as well.

## Purchase Code for Maple Calculator...

Where can I find my purchase code to complete the installation for Maple Calculator? I am not able to use it without one.

## Prove Völler's theorem using Maple...

If you draw a chord in any curve, when the latter becomes infinitely small, the ratio of the surface segment to the triangle formed by the chord and the associated tangents is 2:3.

(Source: Archive of Mathematics and Physics, editor Johann August Grunert, 31st part of 1858, pp. 449-453, "On a remarkable general theorem on curves",
Author: Andreas Völler)

(The curve may be assumed to be sufficiently differentiable.)

## How to debug "main"...

I was about to review a piece of code which is the "main procedure" of a worksheet (as one would say in other languages).

What I mean by that are the top level code statements of a Maple worksheet which are not part of procedures. For the code example I can easily put everything into a procedure and invoke the Maple debugger. For larger worksheets this becomes complicated.

For this reason I was wondering whether the debugger can also be started for a complete document.

## could be or could not be...

I have a quite complex expression (where and are real numbers):

expr := Or(And(-p^2 + 3*q < 0, p < 0, p^2 - 4*q < 0, Or(And(p < 0, -q < 0), p < 0, q < 0), Or(And(-2*p^2 + 3*q < 0, -q^2 < 0), And(p <= 0, Or(-2*p^2 + 3*q < 0, q^2 < 0))), Or(And(Or(And(p < 0, -q < 0), p < 0, q < 0), Or(And(-2*p^2 + 3*q < 0, -q^2 < 0), And(p <= 0, Or(-2*p^2 + 3*q < 0, q^2 < 0)))), And(p < 0, -q < 0), p < 0, q < 0, And(2*p^2 - 3*q < 0, -q^2 < 0), And(-p <= 0, Or(2*p^2 - 3*q < 0, q^2 < 0))), -2*p^5 + 15*p^3*q - 27*p*q^2 <= 0, p^2*q^2 - 4*q^3 = 0), And(p^2 - 3*q = 0, p < 0, -2*p^2 + 3*q < 0, Or(And(p < 0, -2*p^2 + 3*q < 0), p < 0, 2*p^2 - 3*q < 0), 2*p^3 - 9*p*q = 0), And(-p^2 + 3*q < 0, Or(And(p < 0, p^2 - 4*q < 0), p < 0, -p^2 + 4*q < 0), p < 0, -q < 0, Or(And(-2*p^2 + 3*q < 0, -q^2 < 0), And(-p <= 0, Or(-2*p^2 + 3*q < 0, q^2 < 0))), Or(And(p < 0, -q < 0, Or(And(-2*p^2 + 3*q < 0, -q^2 < 0), And(-p <= 0, Or(-2*p^2 + 3*q < 0, q^2 < 0)))), And(p < 0, -q < 0), And(2*p^2 - 3*q < 0, -q^2 < 0), And(p <= 0, Or(2*p^2 - 3*q < 0, q^2 < 0))), 2*p^5 - 15*p^3*q + 27*p*q^2 <= 0, p^2*q^2 - 4*q^3 = 0)):

According to `coulditbe`, is satisfiable:

```_EnvTry := 'hard':
coulditbe(expr) assuming real;
=
true

```

But according to `SMTLIB:-Satisfiable`, is not satisfiable:

```SMTLIB:-Satisfiable(expr) assuming real;
=
false

```

Why are the two results opposite

For reference, below is the output from `RealDomain:-solve`

```RealDomain:-solve(expr);
=
/           1  2\
{ p = p, q = - p  }, {p = p, q = 0}
\           4   /

```

I also tried using `RealDomain:-simplify`, yet the output remains almost unchanged (Why?).

## How to find the dispersion relation?...

How to find the dispersion relation (9). Although I calculated the dispersion relation (see Eq. (3) in DR_1.mw), it is not consistent as in the image.

## Force Maple not to reuse Integration and different...

Is there a way to force maple not to reuse integration constant names or constant names arising from solving a differential equation.

In other words, once maple  provided e.g. an integration constant, then it may not reuse it when I solve another differential equation or integral equation in the same worksheet.

It causes problems with certain problems containing several differential equations that need to be solved sequentially.

## Area Between Curves - Graph...

Good evening, how do I get Maple to graph and shade the intersection area of ​​the curves? Can someone please tell me how to do this? I have used implicitplot but I don't know how to shade the area.

## Centering plots in an array plot...

I'm sure this has been asked and answered, but I can't find the correct MaplePrimes page on it. How does one generate an array plot where the plots are centered within each box and not left justified? I need to make a PDF out of the document with an array plot of 1 column and 2 rows. (The following is just an example.)

## Why Maple says this ode is Bernoulli when it is no...

Bernoulli first order ode has form as show in wikipedia  and also on Maple own site as

Notice that it is P(x)*y above and not P(x)* y^(-1) so the y(x) must be linear in that term.   But when I give Maple this ode

```ode:=diff(y(x),x) + x*y(x)^(-1)= y(x)^(-1);
```

Which is clearly not of the form above, it solves it as Bernoulli.  In the above ode, P(x) is x and Q(x) is 1 and n is -1.

The ode advisor correctly said it is separable. But trace shows it used Bernoulli. Also when asking it to solve it as Bernoulli, it does.

What Am I missing here?  Is it not wrong for Maple to use Bernoulli method on this ode which is not Bernoulli?

Worksheet below

 > interface(version);

 > Physics:-Version();

 > libname;

 > restart;
 > ode:=diff(y(x),x) + x*y(x)^(-1)= y(x)^(-1); IC:=y(1) = 0; DEtools:-odeadvisor(ode);

 > infolevel[dsolve]:=5;

 > dsolve(ode,y(x));  #why this says it solved it as Bernoulli ?

Methods for first order ODEs:

--- Trying classification methods ---

trying 1st order linear

trying Bernoulli

<- Bernoulli successful

 > dsolve(ode,y(x),[Bernoulli])

Classification methods on request

Methods to be used are: [Bernoulli]

----------------------------

* Tackling ODE using method: Bernoulli

--- Trying classification methods ---

trying Bernoulli

<- Bernoulli successful

## How do I fix column vectors not showing properly w...

Dear Maple community,

I was going to export my math assignment about vector functions as an PDF, when I noticed that it butchered every column vector printed out in blue in the document as math-output. I only have this issue when exporting my work.

How do I make Maple display both coordinates of vector in the blue output field?

I produced the below image as an illustration of my problem:

## Why can't a variable in a procedure be called?...

Why can't the variables in my procedure be called? Omega1, Omega2, Q1, Q2 are all expressed in the form of local variables in the loop, why can't we solve the equation because there are too many variables? At the same time, I would like to ask how to output the results of Q1 and Q2?

equation915.mw

## coeff question regarding asymptotic expansions...

Why can the coeff operator return the coefficient of 1/b, namely -1/x in the example below correctly,

but cannot return the coefficient of 1/x , which should be -1/b?

dummy := asympt(x*1/(1 - a*x - b*x^2), x);
coeff(dummy, 1/x);
coeff(dummy, 1/b);

What one generally wants is to be able to return the coefficients of the orders of an asymptotic expansion, but coeff seems unable to do that as soon as you want the coefficients of 1/x^n