## 1491 Reputation

8 years, 233 days

## MaplePrimes Activity

### These are answers submitted by Mariusz Iwaniuk

From here, we have(An example):

with(LinearAlgebra);

A := Matrix([[2, -1], [-1, 2]]);

eigenvalues := Eigenvalues(A);

#Vector[column](2, [3, 1])

Matrix.mw

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## dsolve with no error...

It should be: L[z](0)=0(I assume,of course) not  L[z](0).

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## Hard for symbolic, easy for numerics....

For symbolic solver is hard to find a solution. With numerics it's easy.See attached file.

_equations.mw

## Another ways:...

Another ways:

1.Export to *.obj file and view in Online 3D Viewer.

Export("3dplot.obj", plot3d((x^2+y^2)/sqrt(x^2+y^2), x = -1 .. 1, y = -1 .. 1), base = homedir);

where homedir you can check by command:

kernelopts(homedir);

2.Export to *.stl file and view in Free online STL viewer:

Export("3dplot.stl", plot3d((x^2+y^2)/sqrt(x^2+y^2), x = -1 .. 1, y = -1 .. 1), base = homedir);

Almost is possible by Laplace Transform to find the solution of differenatial equation.

Problem is solving the nonlinear recurrence equation(See in worksheet at the end of page).

To insert Labels use CTRL+L on keyboard.

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## PDEtools...

Probably pdsolve is designed to find only one solution not more.We can find more solution using packages PDEtools:

## Simpler code:...

```int(convert(cos(2*x)/(1+2*sin(3*x)^2), exp), x = 0 .. Pi);

# 0```

## Solution by another math software....

Using Rubi on Mathematica I have got a answer for case 3D.

See attached file for details:

Integral_3D.mw

## ....

To reproduce the computation below in Maple 2018.1 you need to install theMaplesoft Physics Updates (version 134 or higher)

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UPDATED:

Physics package was fixed and now with version 195 works fine.

UPDATED 15.11.2018:

Solution with Physics:-Version 200:

PDE_with_Physics-version_200.mw

Thumb if You like.

## Bug!...

Yes it's a Bug in KroneckerDelta function for m=4 it should be 0 not 1.

with(Physics, KroneckerDelta);

[seq(KroneckerDelta[m, 0], m = 0 .. 10)];

#[1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0]

but It should be: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

See workaround in attached file:

Thumb if You like.

## Workaround....

infolevel[IntegrationTools] := 3;

`assuming`([int(GAMMA(a, s)*exp(-b*s), s = 0 .. infinity)], [a > 0, b > 0]);

#Definite Integration:   Integrating expression on s=0..infinity
Definite Integration:   Using the integrators [distribution, piecewise, series, o, polynomial, ln, lookup, cook, ratpoly, elliptic, elliptictrig, meijergspecial, improper, asymptotic, ftoc, ftocms, meijerg, contour]
IntegralTransform LookUp Integrator:   Integral might be a laplace transform with expr=GAMMA(a,s) and s=b.
LookUp Integrator:   unable to find the specified integral in the table
Definite Integration:   Returning integral unevaluated.

Then we see Maple can't find in Table a Laplace Transform(?) ,but:

inttrans:-laplace(GAMMA(a, s), s, b);#Works fine

#GAMMA(a)*(1-(1+b)^(-a))/b

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