## 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:

## The flag on the strip of Möbius

by: Maple

The flag of Germany on the strip of the German mathematician August Ferdinand Möbius. Basically, it's just one way to represent flags of a certain type. It seemed that the flag looked good on the Mobius strip.
FLAG.mw

## 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

## gridlines do not show on axis when using cmaple.ex...

I am now running eveything in cmaple.exe for number of reasons. But I find the plot generated do not show grid lines as it does in worksheet (GUI).

Below is worksheet I used, and below that the .mpl file used for command line with the command used.

 > interface(version);

 > restart;
 > plot(x, x=0..1, axis=[gridlines=[10, color=blue]]);

 >

Here is the T.mpl file

currentdir("C:/tmp");  #change as needed

#the following commnad below export a plot to a file

plotsetup(ps, plotoutput="t.ps",plotoptions=color,noborder);

p0:=plot(x, x=0..1, axis=[gridlines=[10, color=blue]]):

print(p0); #this will create t.ps in same folder

plotsetup(default); #rest back to default

quit;

Now I run the above as follows

"C:\Program Files\Maple 2024\bin.X86_64_WINDOWS\cmaple.exe"   T.mpl

Next I convert t.ps to t.pdf using Adobt PDF pro. The output is this

You see, there are no grid lines. I tried changing the color to BLUE, but it made no difference. Tried difference colors also. nothing worked.

Is there a way to keep the grid lines when using cmaple.exe?

I also attached  t.pdf converted by adobe from the .ps file. Mapleprime will not let me attached t.ps file.

t.pdf

## Error, (in odetest/series) when calling 'MultiSeri...

Is this new error in Maple? I do not have older versions to check.

Solved this ode as series. When calling odetest on it, it gives this error as shown in worksheet below.

Maple 2024.1.

Any work arounds?

 > interface(version);

 > Physics:-Version();

 > libname;

 > restart;
 > ode:=-(A/( (1-x)*x^4) - B/( x^4*(1-x)^2)+C/( (1-x)*x^2))*y(x)+1/(1-x)*diff(y(x),x)+diff(y(x),x\$2)=0;

 > Order:=3; maple_sol:=dsolve(ode,y(x),'series','point'=1);

 > odetest(maple_sol,ode,'series','point'=1)

Error, (in odetest/series) when calling 'MultiSeries:-multiseries'. Received: 'unable to sort exponents, {(1-B)^(1/2), -(1-B)^(1/2), 1-(1-B)^(1/2), 1+(1-B)^(1/2), 2-(1-B)^(1/2), 2+(1-B)^(1/2), 3-(1-B)^(1/2), 3+(1-B)^(1/2), 4-(1-B)^(1/2), 4+(1-B)^(1/2)}, MultiSeries:-multiseries'

 >

## How can I sort terms of the polynomial after expan...

This is my file

restart;
F := proc(ee, LL) Typesetting:-mrow(InertForm:-Typeset(InertForm:-Display(eval(eval(InertForm:-MakeInert(factor(ee)), [%* = *]) = InertForm:-MakeInert(map(sort, algsubs(a*x = InertForm:-MakeInert(a*x), ee), order = plex(b))), =~([a, b], LL)), inert = false)), Typesetting:-mo("="), InertForm:-Typeset(eval(ee, =~([a, b], LL)))); end proc;
p := a^3*x^3 + 3*a^2*b*x^2*y + 3*a*b^2*x*y^2 + b^3*y^3;
L := [[2, 3], [1, 2], [1/3, -sqrt(2)]];
ans := F~(p, L);
print~(ans);

I get

I want to the order of terms of the polynomial, e.g, (2 x + 3y)^3 like this

(2 x + 3 y)^3 = (2 x)^3 + 3 (2 x)^2 (3 y) + 3 (2 x) (3 y)^2 + (3 y )^ 3 = 8*x^3 + 36*x^2*y + 54*x*y^2 + 27*y^3.

How can I get that

## How to get argument of a solution ...

Solving differential equations, Maple sometimes unfortunately returns the solution in an utterly  unusable form I never encountered a use for.

As an example a solution was found assuming separation of variables. Maple returns the following solution,

Is there a command where I can just get the argument of the solution, namely the differential equation diff(_Y(ts),ts,ts) + etc  ?  or even better as diff(X(ts),ts,ts) + etc   as I intended and expected it to be without the silly and unnecessary proxy variable _Y(ts) ?

It is such a pity that Maple return these results not as a differential equation in F2(ts), but gives the result in a proxy variable which isutterly unnecessary.

Anyway, if anyone knows a command just to get the argument of the solution above to get rid of all the unnecessary and proxy structure, I will appreciate it as I currently copy the solution and redefine it, which can introduce errors and destroys the generality of the document.

## Reproduce a well-known result? ...

A classic result states that the equation x3px2qxr＝0 with real coefficients p, q, r has positive roots iff p＜0, q＞0, r＜0 and -27r2 - 2p(2p2 - 9q)r + q2(p2 - 4q) ⩾ 0 (see for example this question).
However, Maple appears unable to find the condition:

a, b, c := allvalues(RootOf(x^3 + p*x^2 + q*x + r, x), 'implicit'):
RealDomain:-solve({a, b, c} >~ 0, [p, q, r]);
=
Warning, solutions may have been lost
[]



Is there a way to get the above conditions in Maple with as little human intervention as possible (I mean, without a priori knowledge of the theory of polynomials)?

Edit. An interesting problem is when these three positive roots can further be the lengths of sides of a triangle. For reference, here are some (unenlightening) results from some other software:

## How make my plot to have a beter view and which pa...

I don't know how make my graph be beter for real part and imaginary part and abs part which part how work with parameter can any one explain on this example?

G.mw

## How can I put the results of Maple in to a TeX fil...

I have this file

restart:
F := proc(ee,LL)
uses InertForm, Typesetting;
mrow(Typeset(Display(eval(eval(MakeInert(factor(ee)),[%*=*])
=MakeInert(subs(b=MakeInert(b*y)/y,
a=MakeInert(a*x)/x,p)),[a,b]=~LL),
inert=false)),
mo("&equals;"),Typeset(eval(ee,[a,b]=~LL)))
end proc:
p := (a*x)^2 - 2*a*x*b*y + (b*y)^2:
L := [[sqrt(2),3],[2,5],[3,12],[1/3,5/7]];
ans := F~(p, L):
print~(ans):

How can I put the results like this

\documentclass[12pt,a4paper]{article}
\usepackage[left=2cm, right=2cm, top=2cm, bottom=2cm]{geometry}
\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{enumitem}
\theoremstyle{definition}
\newtheorem{ex}{Exercise}
\begin{document}
\begin{ex}
$(\sqrt{2} x-3 y)^2=(\sqrt{2} \cdot x)^2-2 \cdot(\sqrt{2} \cdot x) \cdot(3 \cdot y)+(3 \cdot y)^2=2 x^2-6 \sqrt{2} x y+9 y^2.$
\end{ex}

\begin{ex}
$(2 x-5 y)^2=(2 \cdot x)^2-2 \cdot(2 \cdot x) \cdot(5 \cdot y)+(5 \cdot y)^2=4 x^2-20 x y+25 y^2.$
\end{ex}

\begin{ex}
$(3 x-12 y)^2=(3 \cdot x)^2-2 \cdot(3 \cdot x) \cdot(12 \cdot y)+(12 \cdot y)^2=9 x^2-72 x y+144 y^2.$
\end{ex}

\begin{ex}
$\left(\frac{x}{3}-\frac{5 y}{7}\right)^2=\left(\frac{1}{3} \cdot x\right)^2-2 \cdot\left(\frac{1}{3} \cdot x\right) \cdot\left(\frac{5}{7} \cdot y\right)+\left(\frac{5}{7} \cdot y\right)^2=\frac{1}{9} x^2-\frac{10}{21} x y+\frac{25}{49} y^2.$
\end{ex}

\end{document}