This ode

restart;
ode:=(x+1)*diff(y(x),x)+y(x)^(1/2) = 0;
ic:=y(0) = 1;
sol:=dsolve([ode,ic],y(x))

Direct use of odetest does not give zero.

res:=odetest(sol,ode)

When asking Solve for possible values of x which makes the above zero, it only gave the upper bound

PDEtools:-Solve(res=0,x)

The actual range which makes res=0 is actually -1<x<exp(2)-1

res:=odetest(sol,ode) assuming -1<x,x<exp(2)-1

How could one using Maple obtain this range -1<x<exp(2)-1? 

Mathematica gives the answer using Reduce:

res=Log[Sqrt[x+1]]-1+Sign[Log[(x+1)]-2]*Log[Sqrt[x+1]]-Sign[Log[x+1]-2];
Reduce[res==0,x,Reals]

Is it possible to obtain such result in Maple, since Solve did not give complete answer.

Maple 2020.2

I want to read file dates (for data files) from inside Maple.  Specifically, I want to automate the comparison of access dates.

I thought I'd done this in the past, but my attempt to recreate it has led me to think that I am remembering incorrectly.

Is there a way of doing this?

I don't deeply care about portability (I'm working on Windows 10 and that would be good enough), but since I'm asking the question please comment on the easiest way to make this portable.

I am aware that by default Windows 10 doesn't update the access date.  On the machines I care about, I have changed the configuration so Windows is updating the access date (often enough for my purposes).  I have PowerShell scripts that work correctly.

I have several questions about Grid Toolbox. I am getting into distributed computing for a very large problem I have been working on for a long time; I am working on the simple examples that come with the Grid package, and I am not having much success. I am fairly experienced in Maple but I need help with this. My e-mail is harrisjtster@gmail.com.

How to simplify this trigonometric expression with Maple? I only know the way with  identify command, which is difficult to call mathematically correct:

restart;
Expr:=arctan((1-tan(20*Pi/180))/(1-tan(25*Pi/180)));
evalf[15](Expr);
identify(%);

I do not underand why these two gives different results

restart;
mysol:= exp(sqrt( y(x)^2/x^2+1)) = _C1*x;
ode:=diff(y(x),x) = (y(x)^2+(x^2+y(x)^2)^(1/2)*x)/x/y(x);

And now case A:

simplify(odetest(mysol,ode)) assuming x>0;

                  0

But case B

res:=odetest(mysol,ode):
simplify(res) assuming x>0;

      #does not give zero

Why is putting the result in a variable first makes it give a different result?

What should one do so both case A and B give 0 ?

It looks like scoping issue of assuming. But this is really confusing, I did not expect that putting an intermediate result in a variable first will make a difference.

Maple 2020.2, Physis 897

I'm new to maple ,I have a series of data  which are independent of angle to polarplot. the first coordinate is r, and the second coordinate is f(r,theta). what I want is  to color the figure according to the value of f(r,theta), like the figure below.

the data is listed as follow: 

[[0., 3.], [0.2000000000e-1, 2.960601340], [0.4000000000e-1, 2.922410774], [0.6000000000e-1, 2.885436547], [0.8000000000e-1, 2.849687068], [.1000000000, 2.815170918], [.1200000000, 2.781896852], [.1400000000, 2.749873799], [.1600000000, 2.719110871], [.1800000000, 2.689617363], [.2000000000, 2.661402758], [.2200000000, 2.634476731], [.2400000000, 2.608849150], [.2600000000, 2.584530087], [.2800000000, 2.561529812], [.3000000000, 2.539858808], [.3200000000, 2.519527764], [.3400000000, 2.500547591], [.3600000000, 2.482929415], [.3800000000, 2.466684589], [.4000000000, 2.451824698], [.4200000000, 2.438361556], [.4400000000, 2.426307219], [.4600000000, 2.415673985], [.4800000000, 2.406474402], [.5000000000, 2.398721271], [.5200000000, 2.392427650], [.5400000000, 2.387606862], [.5600000000, 2.384272500], [.5800000000, 2.382438431], [.6000000000, 2.382118800], [.6200000000, 2.383328042], [.6400000000, 2.386080879], [.6600000000, 2.390392334], [.6800000000, 2.396277732], [.7000000000, 2.403752707], [.7200000000, 2.412833211], [.7400000000, 2.423535514], [.7600000000, 2.435876220], [.7800000000, 2.449872265], [.8000000000, 2.465540928], [.8200000000, 2.482899838], [.8400000000, 2.501966977], [.8600000000, 2.522760694], [.8800000000, 2.545299706], [.9000000000, 2.569603111], [.9200000000, 2.595690390], [.9400000000, 2.623581418], [.9600000000, 2.653296473], [.9800000000, 2.684856242], [1., 2.718281828]]

A torus can be defined parametrically by:

where θ, φ are angles which make a full circle, so that their values start and end at the same point, R is the distance from the center of the tube to the center of the torus, r  is the radius of the tube.

R:=10:
r:=5:
plot3d( [ ( R+r(u,v)*cos(v))*sin(u),
          ( R+r(u,v)*cos(v))*cos(u),
            r*sin(v)
        ],
            u=0..2*Pi,
            v=0..2*Pi,style=patchnogrid,
            scaling=constrained,
          scaling=constrained,
coordinateview=[-15..15, -15..15,-5..5],
lightmodel=light3, viewpoint = circleleft);

I set range [-5..5] of the Z axis，but  the range of  Z axis tickmarks  in the above image maybe in [-4.5..4.5] .

How to have tickmarks included at -5 and 5 on the Z axis?

How I can determine coefficiants a0,a1,a2,b0,b1,b2?

Thanks

equation.mw

Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/equation.mw .
 

Download equation.mw

Hello. Please help me find the value of the integral.

Integral.mw

I have tried:

algsubs(Uo/sqrt(GoHo)=Fr, Go Ho/ Uo^2)

(where I want it to yield the answer `1/Fr^2`)

but it just returns:

Go Ho/ Uo^2

I have only just starting using maple , but as far as I can see other possible functions may be solve or eliminate but I believe they aren't relevant here..?

Many thanks for your help !

HOW I CAN FIND A , B DIRECTLY?

NOT BY WRITING RELATION 5?

A.mw

Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/A.mw .
 

Download A.mw

How to write names on an drawing P1, P2, P3, Pn... I try
textplot({seq([(coordinates(point(P[i]))), cat("P", i)], i = 0 .. 5)}, 'align' = {'above', 'left'}):;
i got the message : wrong number of arguments that i don't how correct. Thank you.

Hi,

I would be really grateful if someone can help me in solving the below attached problem in maple.

Thanks in advance.

In Latex 897 correct Latex is generated for the following code. In 905, wrong Latex is generated. This is different from the other cases I posted about (links below) and new issue.

In 897, the Latex generated for this example compiles with no error

restart;
sol:=(Vector(2, [x__1(t),x__2(t)])) = (Vector(2, [2^(3/4)*3^(1/4)*(exp(2^(3/4)*3^(1/4)*t)*_C1-exp(-2^(3/4)*3^(1/4)*t)*_C2-sin(2^(3/4)*3^(1/4)*t)*_C3+cos(2^(3/4)*3^(1/4)*t)*_C4),2*6^(1/2)*(exp(2^(3/4)*3^(1/4)*t)*_C1+exp(-2^(3/4)*3^(1/4)*t)*_C2-sin(2^(3/4)*3^(1/4)*t)*_C4-cos(2^(3/4)*3^(1/4)*t)*_C3)]));
Latex(sol)

Now compiling the Latex gives

\documentclass[11pt]{article}
\usepackage{amsmath}
\usepackage{maplestd2e}  

\begin{document}
\[
\left[\begin{array}{c}x_{1} \! \left(t \right) \\x_{2} \! \left(t \right) \end{array}\right]
 = 
\left[\begin{array}{c}2^{\frac{3}{4}} 3^{\frac{1}{4}} \left({\mathrm e}^{2^{\frac{3}{4}} 3^{\frac{1}{4}} t} \mathit{\_C1} -{\mathrm e}^{-2^{\frac{3}{4}} 3^{\frac{1}{4}} t} \mathit{\_C2} -\sin \! \left(2^{\frac{3}{4}} 3^{\frac{1}{4}} t \right) \mathit{\_C3} +\cos \! \left(2^{\frac{3}{4}} 3^{\frac{1}{4}} t \right) \mathit{\_C4} \right) \\2 \sqrt{6}\, \left({\mathrm e}^{2^{\frac{3}{4}} 3^{\frac{1}{4}} t} \mathit{\_C1} +{\mathrm e}^{-2^{\frac{3}{4}} 3^{\frac{1}{4}} t} \mathit{\_C2} -\sin \! \left(2^{\frac{3}{4}} 3^{\frac{1}{4}} t \right) \mathit{\_C4} -\cos \! \left(2^{\frac{3}{4}} 3^{\frac{1}{4}} t \right) \mathit{\_C3} \right) \end{array}\right]
\]
\end{document}

In 905

The Latex(sol) gives

\documentclass[11pt]{article}
\usepackage{amsmath}
\usepackage{maplestd2e}  

\begin{document}
\[
\left[\begin{array}{c}x_{1} \! \left(t \right) 
\\
 x_{2} \! \left(t \right) \end{array}\right]
 = 
\left[\begin{array}{c}2^{\frac{3}{4}} 3^{\frac{1}{4}} 
\\
\left({\mathrm e}^{2^{\frac{3}{4}} 3^{\frac{1}{4}} t} \textit{\_C1} -{\mathrm e}^{-2^{\frac{3}{4}} 3^{\frac{1}{4}} t} \textit{\_C2} -
\\
\sin \! \left(2^{\frac{3}{4}} 3^{\frac{1}{4}} t \right) \textit{\_C3} +\cos \! \left(2^{\frac{3}{4}} 3^{\frac{1}{4}} t \right) \textit{\_C4} \right) 
\\
 2 \sqrt{6}\, 
\\
\left({\mathrm e}^{2^{\frac{3}{4}} 3^{\frac{1}{4}} t} \textit{\_C1} +{\mathrm e}^{-2^{\frac{3}{4}} 3^{\frac{1}{4}} t} \textit{\_C2} -
\\
\sin \! \left(2^{\frac{3}{4}} 3^{\frac{1}{4}} t \right) \textit{\_C4} -\cos \! \left(2^{\frac{3}{4}} 3^{\frac{1}{4}} t \right) \textit{\_C3} \right) \end{array}\right]
\]
\end{document}

Which when compiled using texlive lualatex gives error. There is a missing \right. 

>lualatex foo5.tex
This is LuaHBTeX, Version 1.12.0 (TeX Live 2020)
 restricted system commands enabled.
(./foo5.tex
LaTeX2e <2020-10-01> patch level 2
.....
..Defaults to "dvips" Driver
(/usr/local/texlive/2020/texmf-dist/tex/latex/graphics/epsfig.sty (/usr/local/texlive/2020/texmf-dist/tex/latex/graphics/graphicx.sty (/usr/local/texlive/2020/texmf-dist/tex/latex/graphics/keyval.sty) (/usr/local/texlive/2020/texmf-dist/tex/latex/graphics/graphics.sty (/usr/local/texlive/2020/texmf-dist/tex/latex/graphics/trig.sty) (/usr/local/texlive/2020/texmf-dist/tex/latex/graphics-cfg/graphics.cfg) (/usr/local/texlive/2020/texmf-dist/tex/latex/graphics-def/dvips.def))))
Defining Automatic Style Generation Macros
Defining Maple Spreadsheet Environments
Maple Spreadsheet and Table Support
) (/usr/local/texlive/2020/texmf-dist/tex/latex/l3backend/l3backend-luatex.def) (./foo5.aux) (/usr/local/texlive/2020/texmf-dist/tex/latex/base/ts1cmr.fd)
! Missing \right. inserted.
<inserted text>
\right .
l.14 \\

?

Maple 2020.2, Physics 905

Fyi, the issues I know about in Latex()  as of now are these 4

https://www.mapleprimes.com/questions/231398-Regression-In-Latex-Between-897-And?sq=231398

https://www.mapleprimes.com/questions/231397-Latex-Latex-Generates-Command-Not-In

https://www.mapleprimes.com/questions/231273-Why-Latex-Fail-To-Convert-Solution

https://www.mapleprimes.com/questions/231262-Latex-Generates-Wrong-Latex-For-This-Example