## How do I integrate in Maple?...

How can I  get the result for the integration when m =n or m is not equal to n and How can I add assumption that m, or n can be even or odd?

 > restart; phi := proc(k,x,L)   if (type(k,even)) then sqrt(2)*sin(Pi*k*x/L)/sqrt(L)   else sqrt(2)*cos(Pi*k*x/L)/sqrt(L)   end if; end proc:
 > Int(phi(m,x,L)*_h^2/m2*diff(phi(n,x,L),x,x),x=-L/2..L/2);
 (1)

## How to adjust 3D view according to 2D?...

My file is working but I want to draw a 2D contour plot into a 3D view. How can I adjust the 3D view as per the 2D plot?

Help_3D_view.mw

## Factor in matrix form...

How can I  change eq13 to eq14 without using op command manually?

## HELP WITH A CORRUPTED FILE ASAP!...

Hey! I need help ASAP, because my maple file has been corrupted and i dont know what to do. Do you guys know how to recover a file? i can save it again as_mw. but should i change it to xml? or how? i have the link to my maple file attached, so if someone can help me, it could be helpful! Because i have an upcoming exam. Thanks youu

## How can a trigonometric expression, including cos(...

Dear All,
I want to simplify the following trigonometric expression, considering that m is an integer number. For this, I use the following command:

expr:= 4*cos(Pi*m)/(Pi*(2*m + 1));
simplify(%, assume=integer);
factor(%);

However, if I want to simplify the following trigonometric expression, m is an integer number, and alpha is a real number, using the following command will lead to the wrong answer because alpha is also considered an integer number. Please guide me.

4*cos(Pi*m+2*alpha*Pi)/(Pi*(2*m + 1));
simplify(%, assume=integer);
factor(%);

Best wishes

## How to make a legend box?...

How can I make a legend for this plot?

plot([17.85*(2.65*t^2 + 1 + 3*t)^2/t^2, 17.85*(2.65*t^2 - 47 + 3*t)^2/t^2, 17.85*(2.65*t^2 - 97 + 3*t)^2/t^2, 17.85*(2.65*t^2 - 147 + 3*t)^2/t^2, 17.85*(2.65*t^2 - 197 + 3*t)^2/t^2], t = 0 .. 25, labels = ['t', 'x'], labelfont = [Times, 12])

I got the following figure.

Now I want to put a legend box in this plot for each color line. How can I do it?

## How to find root from a equation?...

Could anyone please help me to find the root means of the value of x for different values of k in the range 0.1..0.9  by putting the expression P=0 by using the Newton method?

Help_Newton_Method.mw

## Verification problem for power series solutions fo...

Dear Maple community,

I am facing a little problem verifying a power series solution obtained with Maple since the direct substitution back into the PDEs does not seem to be conclusive because the residual contains the powers of independent variables to almost any order.

Please see the enclosed Maple file with a minimal working example:

 > restart:
 > with(DETools):
 > PDE1 := diff(eta(t,x),t) + 1/2*diff(u(t,x),x) + 1/2*eta(t,x)*diff(u(t,x),x) - 1/48*diff(u(t,x),x\$3) + diff(eta(t,x),x)*u(t,x);
 (1)
 > PDE2 := diff(u(t,x),t) + u(t,x)*diff(u(t,x),x) + diff(eta(t,x),x,t,t) + diff(eta(t,x),x) - 1/6*diff(u(t,x),x,x,t);
 (2)
 > sys := rifsimp([PDE1, PDE2]);
 (3)
 > id := initialdata(sys[Solved]);
 (4)
 > sols := rtaylor(sys[Solved], id, point=[t = 0, x = 0], order = 3);
 (5)
 > assign(sols);
 > simplify(PDE1);
 (6)
 > simplify(PDE2);
 (7)

Thanks a lot in advance for any help or suggestions.

Kind regards,

DDe

## How to evaluate an expression for multiple values...

Suppose I have an expression like the following:

h(t, x) :=  (m*t^2 + 6*t - 2*x)^2/(36*g*t^2)


I want to calculate multiple values of t in a single expression. Say, for t:= 1,5,10,15,20. I want to evaluate h(t,x) in vector form. so that I can extract for each t. How to write it?

## Need help regarding fit curve?...

Hello everyone, I am trying to generate a relation for x in terms of lambda by putting my expression (A=0) but do not get the explicit relation. Could anyone please help me generate data points between x=[0..1] and lambda by putting A=0 and then making a polynomial by using the fit curve for x in the term of lambda?

Help_Data_points.mw

## How to define a matrix of partial differential ope...

How do we define a matrix or a vector of the partial differential operator?

## How to compute right eigen vector of a matrix in ...

How to evaluate the right eigenvector of a given matrix in maple?

## Commutator table for infinitesimals...

How to obtain the commutator table of the infinitesimal generators?
Can we obtain a commutator table by using any inbuild command in pdetools?

## How to upload a maple .eps in overleaf...

I got a plot by following the code in Mpale 2022.
restart;
with(plots);
P2 := plot3d(-t^2 + x, t = 0 .. 20, x = 0 .. 400, labels = ['t', 'x', 'rho'], labelfont = [Times, 15], viewpoint = "circleleft", colorscheme = ["ygradient", ["Green", "Purple", "Blue", "Red", "BlueViolet"]]);
plotsetup(ps, plotoutput = "P2");
print(P2);

Then I tried the following code for the overleaf. However, I did not get the desired result.

\documentclass[11pt]{article}
\usepackage{graphicx}
\usepackage{epsfig}

\begin{document}
Plot obtained from Maple 2022. \\

\includegraphics[width=0.9\textwidth]{P2.eps}
\end{document}

plotting_file.pdf

Any help is highly appreciated.
Thanks
Deb

## Why doesn't Maple simplify exponents....

I am wondering why Maple simplifies (x^(1/3))^3 to x ,  but not (x^3)^(1/3) .
I even tried the surd function. I believe the surd function is for real number arguments, so it should simplify to x.

 > restart:
 > f:=x->x^3: g:=x->x^(1/3):
 > f(g(x)); g(f(x));
 (1)
 > simplify((x^3)^(1/3))
 (2)
 > simplify(x^(1/3))^3
 (3)
 > simplify(surd(x^3,3))
 (4)
 > simplify(surd(x,3)^3)
 (5)
 >