## spline options in the SavitzkyGolayFilter...

Hello,

I want to use the spline options in the SavitzkyGolayFilter, but I don't understand the description in the Maple help. Can someone give me Sytax examples? I would also like to specify the 1st and 2nd derivatives of the endpoints.

I am grateful for any help!

## finding if an arbitrary function is always positiv...

I was wondering if there was a command that could tell me if an expression consisting of undermined functions was always positive (with real domain).

For example f1:=f(x)^2+g(y)^4 is always positive.

but f(x)^2-g(y)^2 is only positive on a restricted domain.

## what does tr_is_cos mean? internal exception calli...

This looks like a bug I have not seen before. Any one seen this before?

Error, (in Handlers:-TrigExpOnly) cannot determine if this expression is true or false: tr_is_cos

Can others reproduce it? I am using Maple 2023.2 on windows 10

btw, I found that by doing int(evala(integrand),t) instead of int(integrand,t) then the error goes away but not all the time. Below are two examples. The first where evala() fixes it, but the second it does not fix it.

 > Physics:-Version()

 > interface(version);

 > restart;

 > integrand:=-(((sqrt(3)*sqrt(27983)*I + 276)*(-594 + 6*I*sqrt(3)*sqrt(27983))^(1/3) + 15*I*sqrt(3)*sqrt(27983) + (25*(-594 + 6*I*sqrt(3)*sqrt(27983))^(2/3))/2 + 2265)*(-150 + (-150 + (-594 + 6*I*sqrt(3)*sqrt(27983))^(2/3))*sqrt(3)*I - (-594 + 6*I*sqrt(3)*sqrt(27983))^(2/3) + 24*(-594 + 6*I*sqrt(3)*sqrt(27983))^(1/3))*(150 + (-150 + (-594 + 6*I*sqrt(3)*sqrt(27983))^(2/3))*sqrt(3)*I + (-594 + 6*I*sqrt(3)*sqrt(27983))^(2/3) - 24*(-594 + 6*I*sqrt(3)*sqrt(27983))^(1/3))*((sqrt(3)*sqrt(27983)*I + 276)*(-594 + 6*I*sqrt(3)*sqrt(27983))^(1/3) - 15*I*sqrt(3)*sqrt(27983) - 2265)*exp(-t*((-594 + 6*I*sqrt(83949))^(2/3)/3 + (-594 + 6*I*sqrt(83949))^(1/3) + 50)/(-594 + 6*I*sqrt(83949))^(1/3))*(-594 + 6*I*sqrt(3)*sqrt(27983))^(2/3)*((-594 + 6*I*sqrt(3)*sqrt(27983))^(2/3) + 12*(-594 + 6*I*sqrt(3)*sqrt(27983))^(1/3) + 150)*sin(t)*cos(t))/(10101630528*(sqrt(3)*sqrt(27983)*I - 99)^2*(sqrt(3)*sqrt(27983)*I + 27983/33)*exp(t)) - ((-594 + 6*I*sqrt(83949))^(2/3) + 12*(-594 + 6*I*sqrt(83949))^(1/3) + 150)*(2*I*sqrt(83949)*(-594 + 6*I*sqrt(83949))^(1/3) + 30*I*sqrt(83949) + 25*(-594 + 6*I*sqrt(83949))^(2/3) + 552*(-594 + 6*I*sqrt(83949))^(1/3) + 4530)*(-594 + 6*I*sqrt(83949))^(1/3)*(sqrt(83949)*(-594 + 6*I*sqrt(83949))^(1/3)*I - 15*I*sqrt(83949) + 276*(-594 + 6*I*sqrt(83949))^(1/3) - 2265)*exp(-t*((-594 + 6*I*sqrt(83949))^(2/3)/3 + (-594 + 6*I*sqrt(83949))^(1/3) + 50)/(-594 + 6*I*sqrt(83949))^(1/3))*(8*cos(t)^2/exp(t) - 4/exp(t))/(5196312*(sqrt(83949)*I + 27983/33)*(sqrt(83949)*I - 99)) + ((-594 + 6*I*sqrt(83949))^(2/3) + 12*(-594 + 6*I*sqrt(83949))^(1/3) + 150)*(2*I*sqrt(83949)*(-594 + 6*I*sqrt(83949))^(1/3) + 30*I*sqrt(83949) + 25*(-594 + 6*I*sqrt(83949))^(2/3) + 552*(-594 + 6*I*sqrt(83949))^(1/3) + 4530)*(-150 + (-594 + 6*I*sqrt(83949))^(2/3))*(-594 + 6*I*sqrt(83949))^(2/3)*exp(-t*((-594 + 6*I*sqrt(83949))^(2/3)/3 + (-594 + 6*I*sqrt(83949))^(1/3) + 50)/(-594 + 6*I*sqrt(83949))^(1/3))/(1154736*(sqrt(83949)*I + 27983/33)*(sqrt(83949)*I - 99)*exp(t)):
 > int(integrand,t)

Error, (in Handlers:-TrigExpOnly) cannot determine if this expression is true or false: tr_is_cos

 >

But the trick of using evala() to avoid this error does not always work. Here is an example below. So need to find another workaround for this.

 > restart;

 > interface(version);

 > integrand2:=1/40406522112*I*(-594+6*I*3^(1/2)*27983^(1/2))^(2/3)*exp(t*(5/3*3^(1/2)*2^(1/2) *sin(1/3*arctan(1/99*83949^(1/2))+1/6*Pi)-5*cos(1/3*arctan(1/99*83949^(1/2))+1/ 6*Pi)*2^(1/2)-1))*(150+I*(-150+(-594+6*I*3^(1/2)*27983^(1/2))^(2/3))*3^(1/2)+(-\ 594+6*I*3^(1/2)*27983^(1/2))^(2/3)-24*(-594+6*I*3^(1/2)*27983^(1/2))^(1/3))*( 2265+(276+I*(27983^(1/2)+92)*3^(1/2)-27983^(1/2))*(-594+6*I*3^(1/2)*27983^(1/2) )^(1/3)+5*I*(-151+3*27983^(1/2))*3^(1/2)+15*27983^(1/2))*(2265-25*(-594+6*I*3^( 1/2)*27983^(1/2))^(2/3)+(276+I*(-276+27983^(1/2))*3^(1/2)+3*27983^(1/2))*(-594+ 6*I*3^(1/2)*27983^(1/2))^(1/3)+15*I*(151+27983^(1/2))*3^(1/2)-45*27983^(1/2))*( (-594+6*I*3^(1/2)*27983^(1/2))^(2/3)+12*(-594+6*I*3^(1/2)*27983^(1/2))^(1/3)+ 150)*3^(1/2)*(-150+I*(-150+(-594+6*I*3^(1/2)*27983^(1/2))^(2/3))*3^(1/2)-(-594+ 6*I*3^(1/2)*27983^(1/2))^(2/3)+24*(-594+6*I*3^(1/2)*27983^(1/2))^(1/3))/(I*3^(1 /2)*27983^(1/2)+27983/33)/(I*3^(1/2)*27983^(1/2)-99)^2/exp(t)*sin(t)*cos(t)-1/ 20785248*I*(I*(-594+6*I*3^(1/2)*27983^(1/2))^(2/3)*3^(1/2)+(-594+6*I*3^(1/2)* 27983^(1/2))^(2/3)-150*I*3^(1/2)-24*(-594+6*I*3^(1/2)*27983^(1/2))^(1/3)+150)* exp(5/3*3^(1/2)*sin(1/3*arctan(1/99*83949^(1/2))+1/6*Pi)*2^(1/2)*t-5*cos(1/3* arctan(1/99*83949^(1/2))+1/6*Pi)*2^(1/2)*t-t)*(2265-25*(-594+6*I*3^(1/2)*27983^ (1/2))^(2/3)+(276+I*(-276+27983^(1/2))*3^(1/2)+3*27983^(1/2))*(-594+6*I*3^(1/2) *27983^(1/2))^(1/3)+15*I*(151+27983^(1/2))*3^(1/2)-45*27983^(1/2))*(2265+(276+I *(27983^(1/2)+92)*3^(1/2)-27983^(1/2))*(-594+6*I*3^(1/2)*27983^(1/2))^(1/3)+5*I *(-151+3*27983^(1/2))*3^(1/2)+15*27983^(1/2))*(-594+6*I*3^(1/2)*27983^(1/2))^(1 /3)*3^(1/2)/(I*3^(1/2)*27983^(1/2)+27983/33)/(I*3^(1/2)*27983^(1/2)-99)*(8/exp( t)*cos(t)^2-4/exp(t))+1/13856832*I*(-594+6*I*3^(1/2)*27983^(1/2))^(2/3)*(-450+I *(-150+(-594+6*I*3^(1/2)*27983^(1/2))^(2/3))*3^(1/2)-3*(-594+6*I*3^(1/2)*27983^ (1/2))^(2/3))*exp(t*(5/3*3^(1/2)*2^(1/2)*sin(1/3*arctan(1/99*83949^(1/2))+1/6* Pi)-5*cos(1/3*arctan(1/99*83949^(1/2))+1/6*Pi)*2^(1/2)-1))*(150+I*(-150+(-594+6 *I*3^(1/2)*27983^(1/2))^(2/3))*3^(1/2)+(-594+6*I*3^(1/2)*27983^(1/2))^(2/3)-24* (-594+6*I*3^(1/2)*27983^(1/2))^(1/3))*(2265-25*(-594+6*I*3^(1/2)*27983^(1/2))^( 2/3)+(276+I*(-276+27983^(1/2))*3^(1/2)+3*27983^(1/2))*(-594+6*I*3^(1/2)*27983^( 1/2))^(1/3)+15*I*(151+27983^(1/2))*3^(1/2)-45*27983^(1/2))*3^(1/2)/(I*3^(1/2)* 27983^(1/2)+27983/33)/(I*3^(1/2)*27983^(1/2)-99)/exp(t):
 > int(integrand2,t);

Error, (in Handlers:-TrigExpOnly) cannot determine if this expression is true or false: tr_is_cos

 > int(evala(integrand2),t);

Error, (in Handlers:-TrigExpOnly) cannot determine if this expression is true or false: tr_is_cos

 >

ps. send to Maplesoft support.

## Problem in the answers: What should I do?...

Why aren't all the variables in fin 1 equation?

And the answers are different from the solutions?

 >
 >
 >
 (1)
 >

 (2)
 >
 (3)
 >
 >

 (4)

 (5)
 >
 (6)

## Residue for a function...

Since C2=D1.D1inv should be equal to I. But return is just an expression (see attached). Further, how to obtain residue for a function C2?

residue.mw

## why Chop does not work when there is a symbol?...

MmaTranslator:-Mma:-Chop  does not seem to work as advertised.. It is supposed to work like Mathematica's Chop, but it does not. Is this by design or is it a bug?

```restart;

MmaTranslator:-Mma:-Chop(((1.378834798932344*10^(-15))*I)*t) ;
```

returns the same input (1.378834799*10^(-15))*I*t but

```MmaTranslator:-Mma:-Chop(((1.378834798932344*10^(-15))*I));
```

now returns 0.

But compare to Mathematica:

This makes it not very useful to use if one has to remove all symbols from an expression first, Any workaround? Here is an actual example where I wanted to use it

```ode:=[diff(x(t), t) = -3*x(t) + 4*y(t), diff(y(t), t) = 5*x(t) + 9*z(t), diff(z(t), t) = y(t) + 6*z(t)];
sol:=dsolve(ode):
evalf[16](sol);
```

gives

Gives

{x(t) = (0.8172764110864494 - (7.853170607134887*10^(-16))*I)*c__1*exp((1.894304969211800 - (1.378834798932344*10^(-15))*I)*t) - (1.150854759654687 + (3.398186702482929*10^(-16))*I)*c__2*exp((-6.475677505300665 + (3.730232887526917*10^(-17))*I)*t) + (0.3780227930126823 + (9.268277369231981*10^(-16))*I)*c__3*exp((7.581372536088866 + (1.198480681985453*10^(-15))*I)*t), y(t) = c__1*exp((1.894304969211800 - (1.378834798932344*10^(-15))*I)*t) + c__2*exp((-6.475677505300665 + (3.730232887526917*10^(-17))*I)*t) + c__3*exp((7.581372536088866 + (1.198480681985453*10^(-15))*I)*t), z(t) = (-0.2435641206911610 + (1.431838044809606*10^(-16))*I)*c__1*exp((1.894304969211800 - (1.378834798932344*10^(-15))*I)*t) + (-0.08015596744746927 + (4.286632781083632*10^(-16))*I)*c__2*exp((-6.475677505300665 + (3.730232887526917*10^(-17))*I)*t) + (0.6323620634472722 - (5.261170533293161*10^(-16))*I)*c__3*exp((7.581372536088866 + (1.198480681985453*10^(-15))*I)*t)}

But Chop does not work on this.

Maple 2023.2

## Does there exist a generalized ListTools:-SearchAl...

There seems to be a consensus about using `ListTools:-SearchAll` to locate an item in a list. However, this subroutine does not work on other expressions; A simple instance is that “ListTools:-SearchAll(1, [[1], 1]);” only outputs  while what I need is  (because both “op([1, 1], [[1], 1])” and “op([2], [[1], 1])” are ). And actually, I hope that there is a more general version in Maple.
For example, I intend to do something like

```restart;
expr, elem := ToInert(eval(`print/Diff`)), '_Inert_NAME'("_syslib"):
SearchAll(elem, expr);
```

and

```List:=[[[[cS,[[[cS,cS],cS],[[[cS,cS],[[cK,cK],cS]],cS]]],cS],cS],[[[cS,[[cK,cS],cK]],cK],cS]]:
items:=Or([[[identical(cS),anything],anything],anything],[[identical(cK),anything],anything]):
SearchAll(items,List); ```

In other words, I need all positions of an operand of an expression (cf. `op`).

It may be manually checked that the "indices" of  in  include [5,1,1,2,1,1,1,2,1,2,1,2], [5,1,2,2,1,1,1,1,2,1,2], and [5,2,2,1,1,3,1,2], since

```patmatch(op([5, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2], expr), elem);
=
true

patmatch(op([5, 1, 2, 2, 1, 1, 1, 1, 2, 1, 2], expr), elem);
=
true

patmatch(op([5, 2, 2, 1, 1, 3, 1, 2], expr), elem);
=
true

```

Similarly, after some manual searchs,

```[[1], [1, 1, 1, 2], [1, 1, 1, 2, 2], [1, 1, 1, 2, 2, 1, 2], [2], [2, 1, 1, 2]]:
convert(typematch~(map2(`?[]`, List, `%`), items), `and`);
=
true

```

It turns out that all "indices" in  of  are [1][1,1,1,2][1,1,1,2,2][1,1,1,2,2,1,2][2], and [2,1,1,2].
But isn't there such a  command that can eliminate the need to manually retrieve them?

## How can we prove this equality?...

I'm stucked in trying to prove that rel(n)  is true for each integer n > 1.

 > restart
 > rel := n -> (n-3)^(n/(n-1))*2^(n/(n-1))-((n-1)*2^(n/(n-1))-4*2^(1/(n-1)))*(n-3)^(1/(n-1)) = 0
 (1)
 >

Do you have any idea to do this?

TIA

## calling proc gives a different answer the second t...

Would Any one be able to give some explanation as to why calling a proc, which does not change anything globally but only acts on the input given, returns different answer the second time it is called with the same exact input? I am not able to understand this result at all.

Maple 2023.2 on windows 10.

 > restart;

 > W:=Matrix(3, 3, [[x^(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)*cos(1/2*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))*ln(x)),-x^(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)*sin(1/2*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))*ln(x)),x^(-1/6*(44+12*69^(1/2))^(1/3)+10/3/(44+12*69^(1/2))^(1/3)+2/3)],[x^(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)*(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)/x*cos(1/2*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))*ln(x))-1/2*x^(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))/x*sin(1/2*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))*ln(x)),-x^(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)*(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)/x*sin(1/2*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))*ln(x))-1/2*x^(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))/x*cos(1/2*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))*ln(x)),x^(-1/6*(44+12*69^(1/2))^(1/3)+10/3/(44+12*69^(1/2))^(1/3)+2/3)*(-1/6*(44+12*69^(1/2))^(1/3)+10/3/(44+12*69^(1/2))^(1/3)+2/3)/x],[x^(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)*(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)^2/x^2*cos(1/2*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))*ln(x))-x^(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)*(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)/x^2*cos(1/2*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))*ln(x))-x^(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)*(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)/x^2*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))*sin(1/2*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))*ln(x))+1/2*x^(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))/x^2*sin(1/2*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))*ln(x))-3/4*x^(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))^2/x^2*cos(1/2*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))*ln(x)),-x^(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)*(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)^2/x^2*sin(1/2*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))*ln(x))+x^(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)*(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)/x^2*sin(1/2*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))*ln(x))-x^(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)*(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)/x^2*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))*cos(1/2*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))*ln(x))+1/2*x^(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))/x^2*cos(1/2*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))*ln(x))+3/4*x^(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))^2/x^2*sin(1/2*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))*ln(x)),x^(-1/6*(44+12*69^(1/2))^(1/3)+10/3/(44+12*69^(1/2))^(1/3)+2/3)*(-1/6*(44+12*69^(1/2))^(1/3)+10/3/(44+12*69^(1/2))^(1/3)+2/3)^2/x^2-x^(-1/6*(44+12*69^(1/2))^(1/3)+10/3/(44+12*69^(1/2))^(1/3)+2/3)*(-1/6*(44+12*69^(1/2))^(1/3)+10/3/(44+12*69^(1/2))^(1/3)+2/3)/x^2]]):
 > foo:=proc(W::Matrix,x::symbol)    local W1:=W,W_det,W1_det;    local F:=2*x^3-ln(x):    W_det := LinearAlgebra:-Determinant(W);    #change the first column    W1[1..3,1] := Vector['column']([0,0,F/x^3]):    W1_det := simplify(LinearAlgebra:-Determinant(W1)):    simplify(W1_det/W_det); end proc:
 > foo(W,x);

 > foo(W,x)

 >

## Determinant calculation of 32 by 32 matrix consist...

Hi there

I am using the Determinant() function in maple to calculate the determinant of 32 by 32 matrix consisting of variables like x1,x2, x3... as well as the products of these variables. This determinant calculation works very well less for 16x16 matrices. However in the 32 by 32 case it takes days and still no result (attached and below you can see the matrix) My first question is that problem actually solvable in reasonable time like within 2 days and do you have any advice how I can achieve this goal.

Thx

Rgds

Birol

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## How to change the placement of arrows in a 2-D/3-D...

In an old question, @nm asked how to . While the answer in that question was almost up to the mark, there remains a regret.

As the instance listed below shows, Maple, by default, draws arrows on a rectangular grid (rather than on a hexagonal mesh):

```  # Example of a three-dimensional vector field:
vf__2d := VectorCalculus:-VectorField([sin(x)*(cos(x) + cos(y)),
sin(y)*(cos(x) - cos(y))], 'cartesian'[x, y]):
# Example of a two-dimensional vector field:
vf__3d := VectorCalculus:-VectorField([1 - (sin(u - v) + sin(u - w)),
1 - (sin(v - w) + sin(v - u)),
1 - (sin(w - u) + sin(w - v))], 'cartesian'[u, v, w]):
# Phase portrait.
Student:-VectorCalculus:-PlotVector(vf__2d, (x, y) =~ -Pi .. Pi,
'grid' = [`\$`](25, 2),
'arrows' = 'THICK',
'fieldstrength' = log[63],
'color' = ColorTools:-Color("#0072BD"),
'axes' = "box"(*, …omitted…*));
= ```

Note that I have changed some of the options in order to make the layout of arrows more prominent.
However, according to the help page of Mma's `VectorPoints`, among the following methods of location generation, Mma by default uses Hexagonal for 2D field vectors and FaceCenteredCubic for 3D field vector:

Here is a collection of different settings available in Mma:

So if the requirement is to get the Maple's output looking like Mathematica's (see the beginning), the number and placement of vectors to plot should be thought of as well. In Maple, “the number of vectors” can be controlled by the plot (or plot3d) opinion , but how do I specify “the placement of vectors” (e.g., Mma's "Hexagonal" and "Mesh")?

Although there exists an  chapter in the documentation, randomly positioned arrows do not fit the bill. Is there any workaround?

## why such large difference in dsolve answer using t...

This is linear ode, third order, Euler type and inhomogeneous ode.

If I solve the homogeneous ode only, then ask Maple to give me a particular solution, then add these, I get much much smaller solution which Maple verifies is correct.

Now when asking Maple to solve the original inhomogeneous ode as is, the solution is much more complicated and much longer with unresolved integrals.

Why does not Maple give the simpler solution? Both are verified to be correct.

This is my theory: When asking maple to find only the particular solution, it seems to have used a different and advanced method to find yp. Which is new to me and trying to learn it. It is based on paper "D'Alembertian Solutions of Inhomogeneous Equations (differential, difference, and some other).

Undetermined coefficients method can't really be used on ode's such as this because its coefficients are not constant.

Now, when asking Maple to solve the inhomogeneous ode, it seems to have used variation of parameters method, which results in integrals, which can be hard to solve.

My question is: Why does not Maple give the same much shorter answer when asked to solve the ode as is? Should it not have done so? Any thoughts on why such large difference in answer? Why it did not use the same method to find yp when asked to solve the whole ode as that leads to much smaller and more elegant solution.

ps. debugging this, it uses LinearOperators:-dAsolver:-dAlembertianSolver which is called from ODEtools/particularsol/linear to find yp when calling DETools:-particularsol(ode); but for some reason, it does not do this when asking it to solve the whole ode directly (if it did, then one will expect same answer to result, right?)

Maple 2023.2 on windows 10.

 > restart;
 (1)
 > #the ode ode:=x^3*diff(y(x), x, x, x) + x^2*diff(y(x), x, x) + 2*x*diff(y(x), x) - y(x) = 2*x^3 - ln(x);
 (2)
 > # find y_h yh:=dsolve(lhs(ode)=0);
 (3)
 > #find particular solution yp:=DETools:-particularsol(ode);
 (4)
 > #test particular solution is correct odetest(yp,ode);
 (5)
 > #find general solution = yh+ yp y_general:=y(x)=rhs(yh)+rhs(yp);
 (6)
 > #test general solution is correct odetest(y_general,ode);
 (7)
 > #now solve the ode directly using Maple. Why this solution is much more complicated? y_general_direct_method:=dsolve(ode);
 (8)
 > #test the above odetest(y_general_direct_method,ode);
 (9)
 >