Hello there. I have a simple differential equation (diff(y(x), x)+1)*exp(y(x)) = 4 , in which I want to got a partial solution (find a value of constant) for y(1)=0. How do I do that? I've checked help on pdsolve function and it's too complicated for me to understand something. Examples do not contain anything such simple as that. Thanks in advance.

I have in mind all the real roots of the equation 2*tan(Pi*t^2)-tan(Pi*t)+tan(Pi*t)*tan(Pi*t^2)^2 = 0.

Maple fails with it:

>RealDomain:-solve(2*tan(Pi*t^2)-tan(Pi*t)+tan(Pi*t)*tan(Pi*t^2)^2 = 0, t);

RootOf(tan(_Z)*tan(_Z^2/Pi)^2-tan(_Z)+2*tan(_Z^2/Pi))/Pi

 Even its numerical solution has gaps.

>Digits := 15; a := Student[Calculus1]:-Roots(2*tan(Pi*t^2)-tan(Pi*t)+tan(Pi*t)*tan(Pi*t^2)^2 = 0, t = -2 .. 2);
Warning, some roots are returned as numeric approximations
 [-1.35078105935821, -1.18614066163451, -1.00000000000000, 0, 

   1.00000000000000, 1.28077640640442, 1.68614066163451,    1.85078105935821]

>nops(a);

8

>b := Student[Calculus1]:-Roots(2*tan(Pi*t^2)-tan(Pi*t)+tan(Pi*t)*tan(Pi*t^2)^2 = 0, t = -2 .. 2, numeric);
 [-1.35078105935821, -1.18614066163451, -1.00000000000000, 

   -0.780776406404415, 0., 1.00000000000000, 1.28077640640442, 

   1.68614066163451, 1.85078105935821, 2.00000000000000]
>nops(b);
                               10

whereas 

>plot(2*tan(Pi*t^2)-tan(Pi*t)+tan(Pi*t)*tan(Pi*t^2)^2, t = -2 .. 2);

shows 14 solutions.

The output of the command

>identify(a);

[1/4-(1/4)*sqrt(41), 1/4-(1/4)*sqrt(33), -1, 0, 1, 1/4+(1/4)*sqrt(17), 1/4+(1/4)*sqrt(33), 1/4+(1/4)*sqrt(41)]

suggests a closed-form expression for the roots.

hi

please help me for solve this equations?

thanksazizi.mw
 

Download azizi.mw

I am trying to achieve an intuitive (non-mathematical) understanding of parallel transport on the unit sphere.
A vector parallel transported along a unit sphere's geodesic clearly maintains as constant its initial orientation vis-a-vis the geodesic i.e. with regard to its moving bases vectors.

Dr. Lopez's application "Visualizing a Parallel Field in a Curved Manifold" displays animation of the parallel transport of a vector along a latitude, which is not a geodesic. As seen by an observer moving with it, the vector rotates clockwise with regard to its moving bases vectors. The rate of rotation increases with higher latitudes.

Then to what is the transported vector maintaining parallelism?

I have uploaded a Maple 2016 worksheet Parallel_transport_on_the_unit_sphere.mw which mostly copies Dr. Lopez's application and, for additional clarity, adds the unit sphere, the moving bases vectors and the moving tangent plane to his display.

Trying to write a generat purpose procedure insteat of having 3 or 4 different named procceduers.

Need to determine the input types of say A,B,C

Proc(A,B,C)

1) A,B,C could be for the form 3/2 , 5x-7 , x^2-sqrt(x+3)  i.e numbers or formulas

2) A,B,C could be 2 elenent lists [2,3]  , [5x-6y,8x+2] ,[2,sqrt(3)]  i.e 2D points

3) A,B,C could be 3 element lists as above    i.e 3D points

4) A,B,C could be 2D vectors

5) A,B,C could be 3D vectors

A, B, C will not be of mixed types but would be good to check A, B, C for consistency and if not retrun an error

Looking to calculate output based on

If type 1) ......

elif type 2).....

.

.

elif type 5)...

end if

return.....

end proc

Hello people in mapleprimes,

I want to simplify the next expression which has 1/k as its exponent,

especially, I want to collect for T.　I hope you will teach me how to do it.

(F__X*(Omega+1)/(F__I*(beta-1)*T))^(1/k)*(T/phi)^(beta/k)

If I do as

simplify(%)assuming(symbolic);

the output is

F__X^(1/k)*(Omega+1)^(1/k)*F__I^(-1/k)*T^((beta-1)/k)*(1/(beta-1))^(1/k)*phi^(-beta/k)

But, as all variables has 1/k as its exponent, I want to collect it to (...)^(1/k).

Is this possible?

taro

Hi, I have been trying to solve the Schrodinger equation for harmonic oscillators using dsolve and plot the the wavefunctions for the different energy levels. However I am struggling to plot all the different wavefuntions on the same plot. I also want to normalize the wavefunctions to help compare their shapes and values. Here's my code:- schro := {diff(psi(x), x, x)-(alpha*x^4+x^2-energy)*psi(x) = 0}; // d / d \\ / 4 2 \ \ { |--- |--- psi(x)|| - \alpha x + x - energy/ psi(x) = 0 } \\ dx \ dx // / ic := {psi(3) = 0, (D(psi))(3) = 1}; {psi(3) = 0, D(psi)(3) = 1} schro1 := subs(energy = 3.30687, alpha = .1, schro); soln1 := dsolve(schro1 union ic, {psi(x)}, type = numeric); // d / d \\ / 4 2 \ \ { |--- |--- psi(x)|| - \0.1 x + x - 3.30687/ psi(x) = 0 } \\ dx \ dx // / proc(x_rkf45) ... end; with(plots); [animate, animate3d, animatecurve, arrow, changecoords, complexplot, complexplot3d, conformal, conformal3d, contourplot, contourplot3d, coordplot, coordplot3d, densityplot, display, dualaxisplot, fieldplot, fieldplot3d, gradplot, gradplot3d, implicitplot, implicitplot3d, inequal, interactive, interactiveparams, intersectplot, listcontplot, listcontplot3d, listdensityplot, listplot, listplot3d, loglogplot, logplot, matrixplot, multiple, odeplot, pareto, plotcompare, pointplot, pointplot3d, polarplot, polygonplot, polygonplot3d, polyhedra_supported, polyhedraplot, rootlocus, semilogplot, setcolors, setoptions, setoptions3d, shadebetween, spacecurve, sparsematrixplot, surfdata, textplot, textplot3d, tubeplot] odeplot(soln1, [x, psi(x)], -3 .. 3); Thank in advance

I tried to generate a simple plot based on an expression using units. Please see the screenshot of the worksheet below

The y-axis should be scaled in m³ not m² because a, b and the variable r are in m. I know that it is possible to enforce the axis scaling in units using useunits but since the mathematical definition of the expression is clear this should not be necessary.

The other question is why is the y-axis missing the variable name? On this page on the Online Help http://www.maplesoft.com/support/help/Maple/view.aspx?path=MaplePortal/UnitsInPlots it is mentioned "When you plot an expression, the axes labeling shows the variable names and units." I think what I am plotting is an expression.

I am experimenting with creating help files for  my own package.

I have saved  a package overview file and one package command  file into a help data base as a test usingTools, Help Database, Save as Help Page.

These 2 help pages work in principle as i can find them when I search for them and the command  help page opens from the overview page. I now need to edit them. So I edit the original worksheets and use Tools, Help Database, Save as Help Page to update the data base.

Now Maple will not let me overwrite the original page.The Help file savy you can overwrite. So I have to delete the original page first then resave it back in. This involves reentering all the data again. Topic Alisies and Table of contents.

To say the least this is extremely tedious  vastly innefficient and very error prone. I will have upto say 40 help pages to edit and they will require some expirementing with.

Is there a better way to do this?

Edit:-

Hve added this line the the bottom of the worksheet

makehelp('`Rational Trigonometry`', "Rational Trigonometry Overview Help.mw", " C:\Users\Ronan.Ronan-PC\maple\toolbox\UserHelp\lib\maple.help")

get     Error, (in readline) file or directory does not exist

hi..i have a problem for solving this nonlinear differential equationerror.mw

Download error.mw

please help me

thanks...

The angle unit of the SI system is rad and its dimension is 1. In engineering angles are often scaled in degrees. Maple supports the unit "deg" or "arcdeg". However when calculating with these units it does not convert deg to rad automatically and replace rad by 1. Here is an example:

The result of evalf(B) should be 15.708 (= 5*pi), i.e. a value without dimension, neither arcdeg nor rad. How do I get the correct result?

Dear all!.       

I have an expression with ramdom variables. Can i use NLP to optimize it?. In this case, does Maple take the histogram of theses ramdom variables?. Thank!!!

What is the difference between the Expression Palette and the Layout Palette? First I thought that the Layout Palette is supporting the entering of names with e.g. sub- and superscripts, but I learned (the hard way) that the templates of the Layout Palette are "mathematically active".

What is the meaning of the colours green and violett in both palettes?

Can somebody of Maple users execute the following command

restart; pdsolve({diff(w(x, y, z), x)+diff(w(x, y, z), y, y)+2*(diff(v(x, y, z), x)-(diff(u(x, y, z), y))-2*w(x, y, z)) = diff(w(x, y, z), z, z), 3*(diff(u(x, y, z), x, x))+2*(diff(u(x, y, z), y, y))+2*(diff(v(x, y, z), x, y))+2*(diff(w(x, y, z), y)) = diff(u(x, y, z), z, z), 3*(diff(v(x, y, z), y, y))+2*(diff(v(x, y, z), x, x))+2*(diff(u(x, y, z), x, y))-2*(diff(w(x, y, z), x)) = diff(v(x, y, z), z, z)}, {u(x, y, z), v(x, y, z), w(x, y, z)})

in Maple 2016.1.1 on a powerful comp and report the obtained result as an answer to the question?
 That would be very kind of her/him. Thanks in advance. 

Download pdsolve.mw

I am learning how to use Maple with boundary value ODE. Given this ODE

y''''(x)+ lam* y(x) =0

with some B.C., say  y(0)=0,y'(0)=0,y''(L)=0,y'''(L)=0, where L is length.

I can't figure the correct syntax to use. It seems Maple do not like the syntax I am using, but it works on a second order ODE?

Here is my attempt:

restart;
assume(lam>0); assume(L>0);
bc:=y(0)=0,D[1](y)(0)=0,D[2](y)(L)=0,D[3](y)(L)=0;
dsolve({diff(y(x),x$4)+lam*y(x)=0,bc},y(x));

Error is 

Error, (in evalapply) too few variables for the derivative with respect to the 2nd variable
Error, (in dsolve) found the following equations not depending on the unknowns of the input system: {bc}

But on a simpler second order ODE, the syntax works

restart;
assume(lam>0); assume(L>0);
bc:=y(0)=0,D[1](y)(0)=0;
dsolve([diff(y(x),x$2)+lam*y(x)=0,bc],y(x));

No error. 

Is the syntax I am using in first example wrong? what would be the correct syntax? I googled for long time, and can't find one example that shows how to use BVP with higher order ODE. I am Maple newbie.