## Can someone explain what DESol mean as a solution ...

Hello,

I am fairly new to using the Maple software, so I apologize if my question is completely idiotic. Apologies, also, because I could not manage to enter my code as code. When I pressed the button it made the whole text as a code.

I run the following code to seek -if there are any- analytic solutions for the following differential equation.

odeplus := (r^2+L^2)^(5/2)*(diff(f(r), `\$`(r, 2)))+((15/4)*r*(r^2+L^2)^(1/2)+3*(r^2+L^2)^(5/2)/r)*(diff(f(r), r))+M^2*f(r)/(r^2+L^2)^(5/2)-((5/2)*((r^2+L^2)^(1/2))(l-1)+(55/64)*r^2/(r^2+L^2)^(3/2)+(r^2+L^2)^(5/2)*(l^2+3*l+3/2)/r^2)*f(r)+(((r^2+L^2)^(1/2))(5+(5/2)*l)+(5/8)*r^2/(r^2+L^2)^(3/2)-(r^2+L^2)^(5/2)*(3/2+l)/r^2)*f(r) = 0

and then I do

dsolve(odeplus, f(r))

The solutions that Maple returns is given in terms of DESol. Could anyone try and break it down for me? What is this telling me and if I can indeed from the output obtain analytic solutions? Is this some sort of operator acting on something?

Thank you in advance.

## simplify an equation ...

hi.

According to the fhgure attaceh how i can gain the equation (2-27) . I write the equation (2-26) in maple but I couldnot to gain that result.

If possible to reach equation via maple?

Thanks     (1)  (2)  ## Strange Behavior of DynamicSystems[BodePlot]...

I tried the example in BodePlot help.

restart;
with(DynamicSystems):
sys := TransferFunction( 1/(s-10) ):
BodePlot(sys);

That works OK. But, if I invoke Syrup, the example no longer works.

restart;
with(Syrup);
with(DynamicSystems):
ckt := [V, Rsrc(50), C1(15e-9), L1(15e-6), C2(22e-9), L2(15e-6), C3(22e-9), L3(15e-6), C4(15e-9), 1, Rload(50)];

TF := subs(other, V=1, v[Rload]);
sys := TransferFunction(TF);

BodePlot(sys);
I get a message "not a valid plot structure".  OK, try the example, again.

sys := TransferFunction( 1/(s-10) ):
BodePlot(sys);
I also get the "not a valid plot structure" message.

What am I doing wrong?

## How to i solve this complex integration in Maple?...

Respected sir,

I have attached a file that contain integration . Sir I am unable to solve please give me some hint.

1. I want to get final expression , want to get the value of constant from boundary condition.

2.I want to get the final expression (.......+c1)

3.I will put boundary condition to determine the value of c1

## Euler-method of forces on an airplane...

Struggling a bit with the Euler-method from task d) and further.  ## Fracsym package...

When i am running a code in maple worksheet , one error is shown by maple. My code and error (in bold) is below

Instructional workheet for the FracSym package
G. F. Jefferson and J. Carminati

Read in accompanying packages: ASP, DESOLVII and initialise using the with command:

DESOLVII_V5R5 (March 2011)(c), by Dr. K. T. Vu, Dr. J. Carminati and Miss G.

Jefferson

The authors kindly request that this software be referenced, if it is used

in work eventuating in a publication, by citing the article:
K.T. Vu, G.F. Jefferson, J. Carminati, Finding generalised symmetries of

differential equations
using the MAPLE package DESOLVII,Comput. Phys. Commun. 183 (2012) 1044-1054.

-------------
ASP (November 2011), by Miss G. Jefferson and Dr. J. Carminati

The authors kindly request that this software be referenced, if it is used

in work eventuating in a publication, by citing the article:
G.F. Jefferson, J. Carminati, ASP: Automated Symbolic Computation of

Approximate Symmetries
of Differential Equations, Comput. Phys. Comm. 184 (2013) 1045-1063.

with(ASP);
[ApproximateSymmetry, applygenerator, commutator]
with(desolv);
[classify, comtab, defeqn, deteq_split, extgenerator, gendef, genvec,

icde_cons, liesolve, mod_eq, originalVar, pdesolv, reduceVar, reduceVargen,

symmetry, varchange]

Read in FracSym and initialise using the with command:
FracSym (April 2013), by Miss G. Jefferson and Dr. J. Carminati

The authors kindly request that this software be referenced, if it is used

in work eventuating in a publication, by citing:
G.F. Jefferson, J. Carminati, FracSym: Automated symbolic computation of Lie

symmetries
of fractional differential equations, Comput. Phys. Comm. Submitted May 2013.

with(FracSym);
[Rfracdiff, TotalD, applyFracgen, evalTotalD, expandsum, fracDet, fracGen,

split]

BASIC OPERATORS

The Riemann-Liouville fractional derivatives is expressed in "inert" form using the FracSym routine Rfracdiff.
The explicit formula for the form of these fractional derivatives may be found in I. Podlubny, Fractional differential equations: An introduction to fractional derivatives, fractional differential equations, some methods of their solution and some of their applications, San Diego, 1999.)

Rfracdiff(u(x, t),t,alpha);
alpha
D[t     ](u(x, t))

If the fractional derivative is taken for a product, the generalised Leibnitz rule is used to express the result (the product operator used is &* and is non-commutative).
Rfracdiff(u(x, t)&*v(x,t),t,alpha);
infinity
-----
\
)                          (alpha - n)              n
/     binomial(alpha, n) D[t           ](u(x, t)) D[t ](v(x, t))
-----
n = 0
Rfracdiff(v(x, t)&*u(x,t),t,alpha);
infinity
-----
\
)                          (alpha - n)              n
/     binomial(alpha, n) D[t           ](v(x, t)) D[t ](u(x, t))
-----
n = 0

Fractional derivatives of integer order revert to the MAPLE diff routine.

Rfracdiff(u(x, t)&*v(x,t),t,2);
/ d  / d         \\             / d         \ / d         \
|--- |--- u(x, t)|| v(x, t) + 2 |--- u(x, t)| |--- v(x, t)|
\ dt \ dt        //             \ dt        / \ dt        /

/ d  / d         \\
+ u(x, t) |--- |--- v(x, t)||
\ dt \ dt        //

The FracSym rouine TotalD may also be used to find total derivatives. evalTotalD is then used to evaluate the result (in jet notation). For example,

TotalD(xi[x](x, y),x,2);
2
D[x ](xi[x](x, y))
evalTotalD([%],[y],[x]);
[     / d             \      2 / d  / d             \\
[y_xx |--- xi[x](x, y)| + y_x  |--- |--- xi[x](x, y)||
[     \ dy            /        \ dy \ dy            //

/ d  / d             \\       / d  / d             \\]
+ 2 |--- |--- xi[x](x, y)|| y_x + |--- |--- xi[x](x, y)||]
\ dy \ dx            //       \ dx \ dx            //]

EXAMPLE -  FINDING SYMMETRIES FOR A FRACTIONAL DE

Consider the fractional PDE from: R. Sahadevan, T. Bakkyaraj, Invariant analysis of time fractional generalized Burgers and Korteweg-de Vries equations, J. Math. Anal. Appl. 393 (2012) 341-347.

We use the Rfracdiff routine to express the
alpha
fractional derivative with respect to t:
fde1:=Rfracdiff(u(x, t),t,alpha) = (diff(u(x, t), x,x))+n*(u(x, t))^p*(diff(u(x, t),  x));
alpha             / d  / d         \\            p / d         \
D[t     ](u(x, t)) = |--- |--- u(x, t)|| + n u(x, t)  |--- u(x, t)|
\ dx \ dx        //              \ dx        /

sys1:=[Rfracdiff(u(x, t),t,alpha) = (diff(v(x, t), x)), Rfracdiff(v(x, t),t,alpha) = -u(x, t)*diff(u(x, t),x)];
[   alpha              d              alpha                      / d         \]
[D[t     ](u(x, t)) = --- v(x, t), D[t     ](v(x, t)) = -u(x, t) |--- u(x, t)|]
[                      dx                                        \ dx        /]

We use the the FracSym routine fracDet to find the determining equations for the symmetry for fde1.
NOTE: The fourth argument (some integer at least 1) corresponds to the number of terms to be "peeled off" from the sums which occur in the extended infintesimal function for the fractional derivative. A value of 2 provides a good balance between information for solution of determining equations and speed.

deteqs:=fracDet([sys1], [u, v],[x, t], 2, alpha=(0.1)..1);
Error, (in desolv/PickLHSDerivative) Cannot pick out the left hand side derivatives

Please suggest what problem it may be?

## can maple graph do "point to graph" to create feat...

would like to point to graph then it highlight graph with virtical line

and mark 1 in one of row in one of column in table like data

just like define feature manually for machine learning but using graph

## pdsolve does not work...

why pdsolve does not work?

Q and alpha are constant. I want to find f(x,y).

Thanks  (1)  (2)  ## how to get this decimal numbers?...

0.733333e^-1

0.733333e^-3

0.733333e^-5

0.733333e^-7

no matter what e is , expect to output the same 0.733333

## solution to set of nonlinear equations (transcende...

Hello,

I have a set of nonlinear equations (transcendental) containing variables and one free parameter. I want to solve this system for variables while varying parameter's value. I have tried with fsolve and solve commands keeping fixed the parameter value, but they are not solving yet. Is there any way to solve this system for a range of parameter's value.
The systmem is like this, x,y,z are the variables and 'a' is the parameter:
f1(x,y,z,a)=0,
f2(x,y,z,a)=0,
f3(x,y,z,a)=0.

Many thanks in advance.

## Statistics:-Mean fails...

Hi,

I submit you this strange result:
for somenumerical  values of a, b, c  (a, b, c real and b > a), Maple 2018 is not able to compute the mean of
c*U where U is a Uniform random variable with support [a, b].

 > restart:
 > with(Statistics):
 > interface(version); (1)
 > z := .4070716688*RandomVariable(Uniform(0.12-0.02*0.12, 0.12+0.02*0.12)); Mean(z); > z := .4070716688*RandomVariable(Uniform(a, b)); Mean(z); subs({a=0.12-0.02*0.12, b=0.12+0.02*0.12}, %);   (2)
 >

PLEASE: Maple still fails if I replace  a = 0.12 -0.02*0.12 by its value 0.1174
and b = 0.12+0.02*0.12 by its value 0.1224

This is incomprehensible and could hide a more profound problem.

## How to save Maple variables from worksheet...

Hello everyone, i've a problem working with Maple because i have a really big system of equations and for everything that i have to do with them, for example, collect terms, coefficients, take a lot of time from me. The problem it is when, for example, i wait 30 minutes to take the coefficients from a equation and in the next command Maple might stop, then i have to close and start all over again... My question it is if have anyway to save my file in a way that if i close and re open i dont have to compile all again. Maybe this is pretty obvious but i really dont know how to do it, because if i close my work and open again, i have to compile everything again.

## How to compute inverse of a matrix for solving eig...

I have a eigenvalue problem like:

[FF1]* {w}=N^2 *[FF2] *{w}

[FF1] and [FF2] are a*b matrices (non square matrix) , {w} are vectors(eigenvectors) and the values of N are eigenvalues.

I want to obtain eigenvalues and eigenvectors by computing Moore-Penrose pseudo-inverse of [FF2] and do the procedures below :

[FF2]^-1 * [FF1] *{w} =N^2 *{w}            ,        (assume  [FF2]^-1   is Moore-Penrose pseudo-inverse of [FF2]   )

[FF2]^-1 * [FF1] = [FF3]  ,  ( [FF3] is a b*b matrix- squre matrix)

so  [FF3] *{w}=N^2 *{w}

then I can use LinearAlgebra[Eigenvectors](FF3) to get eigenvalues and eigenvectors.

I know that Moore-Penrose pseudo-inverse of [FF2] * [FF1] isn't equal to Identity matrix. [FF2]^-1 * [FF1] <> [ I ] . But assume it can be. ( I have a solution for this problem) .

My biggest problem is [FF2] and [FF1] are large-scale sparse matrix and it takes hours or several days that maple can compute Moore-Penrose pseudo-inverse of [FF2]  and also LinearAlgebra[Eigenvectors](FF3).

Main question : can I compute Moore-Penrose pseudo-inverse and LinearAlgebra[Eigenvectors]  by using Parallel Programming?  if the answer is yes , how? give me an example please.

if the answer is No , is there any way (any algorithm) to find the inverse of a large non-sqaure matrix or eigenvalues of a large matrix faster?

please introduce some books for parallel programming in maple or general.

Thanks.

1.mw