## unable to integral in dsolve...

Hi. what is reason maple unable to integral in answer of dsolve? when I try to use dsolve for solve my equation in answer of maple there are expressions of integral that isnot calculated

&int;(-625 R^2 ro (-2 cp3 x1 lambdaopt+sin((pi t)/10) cp2+(16 cp2)/5) (-cos((pi t)/10)+cos(2 pi)+((-t/5+4) x1+(8 t)/25-32/5) pi) lambdaopt pi b11 (e)^(-((16+5 sin((pi t)/10)) cp1)/(10 lambdaopt x1))+625 (-R^2 k11 (cos((pi t)/10))^3+k11 R^2 (cos(2 pi)-((t-20) (x1-8/5) pi)/5) (cos((pi t)/10))^2+((32 sin((pi t)/10) R^2 k11)/5+(281 R^2 k11)/25+4 lambdaopt^2 (a11 x1+a13 x3)) cos((pi t)/10)-(32 k11 R^2 (cos(2 pi)-((t-20) (x1-8/5) pi)/5) sin((pi t)/10))/5+(281 (x1-8/5) (R^2 k11+(100 lambdaopt^2 (a11 x1+a13 x3))/281) pi t)/125) x1^2)&DifferentialD;t

## help in finding why this code gives 1/0...

I am using code given in https://www.mapleprimes.com/questions/227270-Is-It-Possible-To-Tell-Maple-NOT-To  which is meant to check if the solution returned by pdsolve is trivial or not.

The code works well for many cases, but I just found few cases (10 cases so far) where it gives 1/0 and not able to figure why

running in the debugger shows it gives this error in the "depvars" function.

Since this is a useful function and I need to use it, is there a way to fix this problem? I am posting this as new question instead of a follow up to original old question as I thought this will make it easier for everyone.

Maple 2019.1

 > restart;
 > depvars:= (pde::{algebraic, `=`(algebraic), {set,list}(algebraic, `=`(algebraic))})->    indets(       indets(convert(pde, diff), specfunc(diff)),       And(typefunc(name, name), Not(typefunc({mathfunc, identical(diff)})))    ): is_solution_trivial:= (pde, sol::{`=`, set(`=`),`function`})->    evalb(eval(`if`(sol::set, sol, {sol}), depvars(pde)=~ 0) = {0=0}):
 > pde := diff(w(x,y),x)-( diff(f(x),x)*y^2 -f(x)*g(x)*y+ g(x))*diff(w(x,y),y) = 0;

 > sol:=pdsolve(pde,w(x,y));

 > is_solution_trivial(pde,sol)

Error, (in eval/Int) numeric exception: division by zero

 >

## why subs(AllSolutions=(), sol) seems to corrupt t...

I was trying the command sol:=subs(AllSolutions=(), sol):  given in

https://www.mapleprimes.com/questions/227232-A-New-Problem-In-Latex-Command

On a PDE output and I find the result very surprising:

 > restart;
 > pde:= diff(u(x,t),t)= u(x,t)*(1-u(x,t))+ diff(u(x,t),x\$2): sol:=PDEtools:-TWSolutions(pde,u(x,t));

 > sol:=subs(AllSolutions=(), sol): sol;

 >

What happened to the sol ?  why it says 1=...

Note that Maple returns the solution as expression sequence.  If instead the call was like this

sol:=subs(AllSolutions=(), [sol]):

Then the problem goes away!  and sol remains the same as expected.

Maple 2019.1

How could this be explained>?

## trigonometric of error functions...

Hi all

trying to find analytically sin(erf(t)) and cos(erf (t)) rather than numerically

## lastexception and typesetting...

1/0;
Error, numeric exception: division by zero
lastexception;
0, "numeric exception: division by zero"
lastexception; # ???
Typesetting:-Typeset, "invalid input: %1 expects %2 arguments, but received %3", type, 2, 3

So, printing lastexception produces a new error!
When typesetting=standard, it's OK.

## Error, () too many levels of recursion...

Hi, I have a procedure named f1. In it, it calls another procedure f couple of times. procedure f does not have recursive calls implemented.

I have no idea what caused the error. Could anyone give a hint?

Best,

Jie

## Table and sketches inside table not shown in full ...

I like Maple the most for calculation of difficult parts. But when it comes to display, I am ignorant and do not know how to command the maple for showing me what is visible in the document.

I attach herewith my document which shows in print view only top half of the sketch. What should I do to show all three figures in the portrait page.
(Here below, after uploading it is shown alright, but in the print preview it is not showing!!).

I want to convert the doc to pdf. Therefore, in the doc preview itself it should be complete.

Thanks for help.

Ramakrishnan V

## General Procedure For Array Interpolation ...

So, I am trying to write a method for array interpolation. I have a Matrix that is X by 3, where each column holds specific data (column 1 holds independent data 1, column 2 holds independent data 2, column 3 holds dependent data).

This data comes from a function with 2 independent variables, and I am creating a graph of this function, basically, with both independent variables going from 0 to 1 (approximately 300 values per variable, giving me a matrix with 90k values already). My goal is to use interpolation to get a lot of values in between the points I already calculated.

That being said, I don't know how to use the ArrayInterpolation command to achieve this. I will post my code below if anyone can help me out!

Code:

Interpolate := proc(M::Matrix)
local i; local j;
local M1 := Matrix(RowDimension(M),1);
local M2 := Matrix(RowDimension(M),1);
local M3 := Matrix(RowDimension(M),1);
for i from 1 to RowDimension(M) do
M1(i) := M(i,1);
M2(i) := M(i,2);
M3(i) := M(i,3);
end do;
print(M1,M2,M3);
local M4 := Matrix(1000,1);
local M5 := Matrix(1000,1);
for j from 1 to 1000 do
M4(j,1) := 0.001*j;
M5(j,1) := 0.001*j;
end do;
ArrayInterpolation([M1,M2],M3,[M4,M5]);
end proc;

## replace function u__0(r, theta, t) with f[1, 1](r,...

How I can replace  u__0r, theta, t) with f1, 1(r, theta) in attached file.

I want in I have only f1,1] function.

Thanks

 >
 (1)
 >
 (2)

## Internal Error in Typesetting invalid object...

Hi, my codes ran smoothly well until I changed some assignment value. It reported invalid object error.

Error, Got internal error in Typesetting:-Parse:-Postprocess : "internal error: invalid object "

Part of the codes are as follows:

""sigma:=0.00002:    m:=5:   n:=4:
Error, Got internal error in Typesetting:-Parse:-Postprocess : "internal error: invalid object "

Could anyone give some hints on what goes wrong here? It seems to be a configuration issue but I completely have no clue..

Best,

Jie

## how to handled mixed conditions ?...

How 2 solve summation when M,  Z,  X are given with mixed conditions?

## How do I sovle Double integration of function cont...

restart;

##########  omega and theta are variables,where J[3],F[2],H[2],etc are constants.

t1:=-1/(-16.*omega^2+exp(-4*omega)+exp(4*omega)-2.)*(-(0.5817764173e-1*I)*exp((2/9)*omega*cos(theta))*omega^5*cos(theta)*J[3]-(.6981317009*I)*exp((2/9)*omega*cos(theta))*omega^4*cos(theta)*H[3]-0.4524927691e-1*exp(.2222222222*omega*(cos(theta)-9.))*cos(theta)*omega^3*G[3]-.6205615118*exp(.1111111111*omega*(2.*cos(theta)-9.))*cos(theta)*omega^3*H[2]+.6205615118*exp(.1111111111*omega*(2.*cos(theta)-9.))*cos(theta)*omega^3*F[2]+.9308422676*exp(.2222222222*omega*(cos(theta)-9.))*cos(theta)*omega^4*H[3]-.1034269187*exp(.1111111111*omega*(2.*cos(theta)-9.))*cos(theta)*omega^3*G[2]-0.7757018900e-1*exp(.1111111111*omega*(2.*cos(theta)-9.))*cos(theta)*omega^2*G[2]-0.7757018898e-1*exp(.2222222222*omega*(cos(theta)-9.))*cos(theta)*omega^4*J[3]-0.9696273622e-1*exp(.2222222222*omega*(cos(theta)-9.))*cos(theta)*omega^3*J[3]-0.4524927691e-1*exp(.2222222222*omega*(cos(theta)-9.))*cos(theta)*omega^2*J[3]-.2714956613*exp(.2222222222*omega*(cos(theta)-9.))*cos(theta)*omega^2*H[3]-0.7757018898e-1*exp(.2222222222*omega*(cos(theta)-9.))*cos(theta)*omega^4*G[3]+0.8726646261e-1*exp((2/9)*omega*cos(theta))*omega^3*J[3])*cos((2/9)*omega*sin(theta));

t2:=int(int(t1,omega=0..infinity),theta=0..2*Pi);

## Maple Cloud problem...

Problem copying a document to Maple Cloud (Public domain)

• Verified email is correct

• Chose File → Save to Cloud... (or clicked Send Document to Cloud on Maple Cloud palette) either way opend Login dialog

• Entered  Account = Maplesoft account, my Email and password then clicked Log in.  The following message appears: "The account type or email address or password is incorrect"

I've saved .mw files to Maple Cloud before with no problems.  Any help appreciated.

Thanks, Les

## Phase portrait ...

I have the equation (𝑑𝑥/𝑑𝑡)^2=𝑎𝑥^3+𝑏𝑥^2+𝑐𝑥+𝑑.

How do I plot 𝑑𝑥/𝑑𝑡 against x? (as the coefficients a, b, c and d vary)

I expect it looks like the following graph:

## Why does Maple's adjoint function not flip the sig...

Hello,

I'm confused about Maple's adjoint function (in the DEtools package). When I take the adjoint of the derivative operator: