## solve the equation of the odometric model...

Hello, I try to solve the equations of the odometric model with the Maple 2024 but I have not the answers as with the hands, can you help me to verify it ?

dsolve(diff(phi(t), t) = tan(10*t)/5)

dsolve(diff(x(t), t) = V*cos(ln(1 + tan(10*t)^2)/100))

dsolve(diff(y(t), t) = V*sin(ln(1 + tan(10*t)^2)/100))

Best regards, Edern Ollivier.

## Need to Obtain Bifurcation Points and Bifurcation ...

Hello Everyone;

I need to find the bifurcation point and further bifarcation diagram for the given model. But facing error. Can anybody help to do this? Can you refer some library for bifurcation analysis of ODE's? Code is attched. Thanks in Advance.

123.mw

 >
 >
 >
 (1.1)
 >
 (1.2)
 > bif_eq1 := eq1 = 0;

 > bif_eq2 := diff( eq1, V) = 0;

 > bif_sol := solve({ bif_eq1,bif_eq2}, {V, g_Na});

as the solutions, which are then expressed as the points  via

## what is the right way to rearrange this equation...

I have solution to system of equations that results (I assign it to) in:

```I2sol := -I*omega0*k*L*vin*1/(L^2*k^2*omega0^2 + R^2)
```

I then try to solve it for k by doing

```solve(I2sol = I2, k)
```

but that doesn't work.  What is the "right" Maple way to rearrange I2 such that the expression is the solution(s) for k?

## HELP WITH A CORRUPTED FILE ASAP!...

Hey! I need help ASAP, because my maple file has been corrupted and i dont know what to do. Do you guys know how to recover a file? i can save it again as_mw. but should i change it to xml? or how? i have the link to my maple file attached, so if someone can help me, it could be helpful! Because i have an upcoming exam. Thanks youu

## why mapleprimes removes tags from post?...

I noticed tags on the post

https://mapleprimes.com/questions/238161-Why-Maple-Gives-Solution-To-Euler-Ode

keep disappearing.

I added tags "differential equation" and "dsolve" and so on.

Later on when I visit this site again I found the tags are all gone.

Why does Mapleprimes remove the tags on post?

Or is someone else removing the tags? If so, why? is something wrong with the tags I've added?

This happend twice on this one post. I noticed earlier today the tags were gone, so I added them again. And now I see the same thing. They are all gone.

## Kernel Issues in Maple Flow...

I am new to Maple Flow and am constantly having issues like the one shown below. A cell will become corrupted somehow, and the kernel will crash or freeze. I can save and quit, but if I re-open the file, the crash will happen again before I can diable evaluation. My questions:

1. Has anyone else had this issue? Was it solvable?
2. Can evaluation be disabled by default? Its possible in Maple but I don't see how in Flow.
3. Can the kernel be restarted and reconnected (like Jupyter Lab)?

I cant expand the cell in question because of the crash, but this cell isn't the issue. This is happening all the time.

## Problem bug in Maple Primes with Replys ...

I have noticed over a few questions I have asked recently.
I ask a question.                   It goes to top of active converstaions

A bit of time passes  so slides  of the top six/seven that show

Another Reply/Answer from someone                possibly does not show in active conversations.  I catch this by the orange flag or email notification

I reply                                 Does not appear in active conversations..

This can kill the conversation chain.

I have even tried changing one of me replys to an answer but did not go to top active conversations again.

Has anyone else expperienced this?

## How to list all known types...

If a type is not known, an error is thrown

```type([],foo)
Error, type `foo` does not exist
```

Since no error is thrown, these types are known

```type({},'{}');# why that output?
false

type([],'[]')
true

```

I would have expceted {} and [] to be listed as subtypes of set and list since their counterparts (nonemptylist and nonemptyset) exist. Technically the types {} and [] are not needed since negating

```not(type([],nonemptylist));
not(type({},nonemptyset));
true

true

```

works.  However, the types exist, hence my question

## Center and radiius of a circle in 3d...

restart;
_local(D, O);
with(Student:-MultivariateCalculus);
A := [0, 0, 0];
B := [a, 0, 0];
C := [a, b, 0];
D := [0, b, 0];
S := [0, 0, h];
O := [x, y, z];
lineSC := Line(S, C);
lineSD := Line(S, D);
H := Projection(A, lineSC);
K := Projection(A, lineSD);
OH := H - O;
OK := K - O;
OC := C - O;
M := Matrix([OH, OK, OC]);
O := eval(O, %);
R := simplify(Distance(O, H));
O

Student:-MultivariateCalculus:-LineApplyFunction([0,0,h],

[Typesetting:-mtable(Typesetting:-mtr(Typesetting:-mtd(a,

rowalign = "", columnalign = "", groupalign = "",

rowspan = "1", columnspan = "1"), rowalign = "",

columnalign = "", groupalign = ""), Typesetting:-mtr(

Typesetting:-mtd(b, rowalign = "", columnalign = "",

groupalign = "", rowspan = "1", columnspan = "1"),

rowalign = "", columnalign = "", groupalign = ""),

Typesetting:-mtr(Typesetting:-mtd(uminus0h, rowalign = "",

columnalign = "", groupalign = "", rowspan = "1",

columnspan = "1"), rowalign = "", columnalign = "",

groupalign = ""), foreground = "[0,0,0]", readonly = "false",

align = "axis", rowalign = "baseline", columnalign = "center",

groupalign = "{left}", alignmentscope = "true",

columnwidth = "auto", width = "auto", rowspacing = "1.0ex",

columnspacing = "0.8em", rowlines = "none",

columnlines = "none", frame = "none",

framespacing = "0.4em 0.5ex", equalrows = "false",

equalcolumns = "false", displaystyle = "false", side = "right",

minlabelspacing = "0.8em")],variables=[x,y,z],parameter=t,id=1)

Student:-MultivariateCalculus:-LineApplyFunction([0,0,h],

[Typesetting:-mtable(Typesetting:-mtr(Typesetting:-mtd(0,

rowalign = "", columnalign = "", groupalign = "",

rowspan = "1", columnspan = "1"), rowalign = "",

columnalign = "", groupalign = ""), Typesetting:-mtr(

Typesetting:-mtd(b, rowalign = "", columnalign = "",

groupalign = "", rowspan = "1", columnspan = "1"),

rowalign = "", columnalign = "", groupalign = ""),

Typesetting:-mtr(Typesetting:-mtd(uminus0h, rowalign = "",

columnalign = "", groupalign = "", rowspan = "1",

columnspan = "1"), rowalign = "", columnalign = "",

groupalign = ""), foreground = "[0,0,0]", readonly = "false",

align = "axis", rowalign = "baseline", columnalign = "center",

groupalign = "{left}", alignmentscope = "true",

columnwidth = "auto", width = "auto", rowspacing = "1.0ex",

columnspacing = "0.8em", rowlines = "none",

columnlines = "none", frame = "none",

framespacing = "0.4em 0.5ex", equalrows = "false",

equalcolumns = "false", displaystyle = "false", side = "right",

minlabelspacing = "0.8em")],variables=[x,y,z],parameter=t,id=2)

/     2            2         / 2    2\ /
|    h  a         h  b     h \a  + b / |
HAssign|------------,------------,------------|
| 2    2    2  2    2    2  2    2    2|
\a  + b  + h  a  + b  + h  a  + b  + h \

/    2         2  /
|   h  b    h b   |
KAssign|0,-------,-------|
|   2    2  2    2|
\  b  + h  b  + h \

/                2                       2
|               h  a                    h  b
OHAssign|uminus0x + ------------,uminus0y + ------------,uminus0z
|            2    2    2             2    2    2
\           a  + b  + h             a  + b  + h

/ 2    2\ /
h \a  + b / |
+ ------------|
2    2    2|
a  + b  + h \

/                      2                    2  /
|                     h  b               h b   |
OKAssign|uminus0x,uminus0y + -------,uminus0z + -------|
|                     2    2             2    2|
\                    b  + h             b  + h \

OCAssign(uminus0x + a,uminus0y + b,uminus0z)

M := Matrix(3, 3, {(1, 1) = Typesetting:-mrow(Typesetting:-mo("&\

uminus0;"), Typesetting:-mi("x"), Typesetting:-mo("&plus;"),

Typesetting:-mfrac(Typesetting:-mrow(Typesetting:-msup(Typese\

tting:-mi("h"), Typesetting:-mn("2")), Typesetting:-mo("&Invis\

ibleTimes;"), Typesetting:-mi("a")), Typesetting:-mrow(Typeset\

ting:-msup(Typesetting:-mi("a"), Typesetting:-mn("2")),

Typesetting:-mo("&plus;"), Typesetting:-msup(Typesetting:-mi(\

"b"), Typesetting:-mn("2")), Typesetting:-mo("&plus;"),

Typesetting:-msup(Typesetting:-mi("h"), Typesetting:-mn("2"))\

))), (1, 2) = Typesetting:-mrow(Typesetting:-mo("&uminus0;"),

Typesetting:-mi("y"), Typesetting:-mo("&plus;"), Typesetting:\

-mfrac(Typesetting:-mrow(Typesetting:-msup(Typesetting:-mi("h"\

), Typesetting:-mn("2")), Typesetting:-mo("&InvisibleTimes;"),\

Typesetting:-mi("b")), Typesetting:-mrow(Typesetting:-msup(Ty\

pesetting:-mi("a"), Typesetting:-mn("2")), Typesetting:-mo("&p\

lus;"), Typesetting:-msup(Typesetting:-mi("b"), Typesetting:-m\

n("2")), Typesetting:-mo("&plus;"), Typesetting:-msup(Typesett\

ing:-mi("h"), Typesetting:-mn("2"))))), (1, 3) = Typesetting:-\

mrow(Typesetting:-mo("&uminus0;"), Typesetting:-mi("z"),

Typesetting:-mo("&plus;"), Typesetting:-mfrac(Typesetting:-mr\

ow(Typesetting:-mi("h"), Typesetting:-mo("&InvisibleTimes;"),

Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-msup(Type\

setting:-mi("a"), Typesetting:-mn("2")), Typesetting:-mo("&plu\

s;"), Typesetting:-msup(Typesetting:-mi("b"), Typesetting:-mn(\

"2"))))), Typesetting:-mrow(Typesetting:-msup(Typesetting:-mi(\

"a"), Typesetting:-mn("2")), Typesetting:-mo("&plus;"),

Typesetting:-msup(Typesetting:-mi("b"), Typesetting:-mn("2"))\

, Typesetting:-mo("&plus;"), Typesetting:-msup(Typesetting:-mi\

("h"), Typesetting:-mn("2"))))), (2, 1) = Typesetting:-mrow(Ty\

pesetting:-mo("&uminus0;"), Typesetting:-mi("x")), (2, 2) =

Typesetting:-mrow(Typesetting:-mo("&uminus0;"), Typesetting:-\

mi("y"), Typesetting:-mo("&plus;"), Typesetting:-mfrac(Typeset\

ting:-mrow(Typesetting:-msup(Typesetting:-mi("h"),

Typesetting:-mn("2")), Typesetting:-mo("&InvisibleTimes;"),

Typesetting:-mi("b")), Typesetting:-mrow(Typesetting:-msup(Ty\

pesetting:-mi("b"), Typesetting:-mn("2")), Typesetting:-mo("&p\

lus;"), Typesetting:-msup(Typesetting:-mi("h"), Typesetting:-m\

n("2"))))), (2, 3) = Typesetting:-mrow(Typesetting:-mo("&uminu\

s0;"), Typesetting:-mi("z"), Typesetting:-mo("&plus;"),

Typesetting:-mfrac(Typesetting:-mrow(Typesetting:-mi("h"),

Typesetting:-mo("&InvisibleTimes;"), Typesetting:-msup(Typese\

tting:-mi("b"), Typesetting:-mn("2"))), Typesetting:-mrow(Type\

setting:-msup(Typesetting:-mi("b"), Typesetting:-mn("2")),

Typesetting:-mo("&plus;"), Typesetting:-msup(Typesetting:-mi(\

"h"), Typesetting:-mn("2"))))), (3, 1) = Typesetting:-mrow(Typ\

esetting:-mo("&uminus0;"), Typesetting:-mi("x"), Typesetting:-\

mo("&plus;"), Typesetting:-mi("a")), (3, 2) = Typesetting:-mro\

w(Typesetting:-mo("&uminus0;"), Typesetting:-mi("y"),

Typesetting:-mo("&plus;"), Typesetting:-mi("b")), (3, 3) =

Typesetting:-mrow(Typesetting:-mo("&uminus0;"), Typesetting:-\

mi("z"))})

Error, invalid input: eval received Matrix(3, 3, {(1, 1) = -x+h^2*a/(a^2+b^2+h^2), (1, 2) = -y+h^2*b/(a^2+b^2+h^2), (1, 3) = -z+h*(a^2+b^2)/(a^2+b^2+h^2), (2, 1) = -x, (2, 2) = -y+h^2*b/(b^2+h^2), (2, 3) = -z+h*b^2/(b^2+h^2), (3, 1) = -x+a, (3, 2) = -y+b, (3, 3) = -z}), which is not valid for its 2nd argument, eqns
/     1       / 2  2      2        2  2    2  2    2  2
R := |------------ \a  h  - 2 a  h z + a  x  + a  y  + a  z
| 2    2    2
\a  + b  + h

2      2  2      2        2  2    2  2    2  2
- 2 a h  x + b  h  - 2 b  h z + b  x  + b  y  + b  z

2      2  2    2  2    2  2\\
- 2 b h  y + h  x  + h  y  + h  z /|^(1/2)
|
/
Why this error ? Thank you.

## How do I solve an invalid subscript selector in my...

I keep getting an error: invalid subscript selector on specifically this part of my code:

MuligIndgange := subsop(RemoveList\[i\]=NULL, MuligIndgange).
Whenever I comment out the MuligIndgange := part it works.

I can't for the life of me see why it's happening, and whenever I use this code outside my proc it works aswell.

Any help is appreciated, and if you need more context I'll be happy to give it.

for i to numelems(MuligIndgange) do
if M1[MuligIndgange[i][1], MuligIndgange[i][2]] =/= 0 then
RemoveList := [op(RemoveList), i];
end if;
end do;
for i from numelems(RemoveList) by -1 to 1 do
MuligIndgange := subsop(RemoveList[i] = NULL, MuligIndgange);
end do;

## What causes multiple ">" symbols in one block...

I have seen this quite a bit in blocks of code. The `>` symbol seems to appear erratically. I don't know how to specifically reproduce this. Does it mean something? I would post the worksheet but it will not run without the package.

## How to make (if possible) this procedure ThreadSaf...

Hello

I have the following procedure that uses the Lie Derivatives of a vector field to build a set of equations.

```LieDerList:=proc(h::symbol,f::list,vars::list)
description "This function returns the system of equations based on the Lie derivative.":
local i,n:=numelems(vars),L:=Array(0..n):
L[0]:=h:
for i from 1 to n do
L[i]:=inner(f,map((a,b) -> diff(b,a),vars,L[i-1])):
end do:
return(zip((w,v)->simplify(w-v),[seq(L)],[seq](cat(h,i),i=0..n))):
end proc:
```

Below it is an example on how to call the procedure.

I used CodeTools:-ThreadSafetyCheck to check all the procedures used within LieDerList and LieDerList itself, but nothing wrong came out. However when I try to run

`LieEq4:=Threads:-Map(w->LieDerList(x,w,[x,y,z]),models4):`

where models4 is a list of 1765 elements, maple returns "Error, (in factors) attempting to assign to `LinearAlgebra:-Modular:-Create` which is protected". If I change Threads to Grid, there is no problem at all.

What am I overlooking? Is there a method to ensure the procedure is thread-safe?

Many thanks.

PS.  I found one problem - inner, which is related to LinearAlgebra package, is not thread-safe.

## Why does Statistics:-Mean fails computing the mean...

For a lesson I'm preparing, I want to illustrate some probability concepts using Maple.
In particular, I need to use the fact that the Expectation operator(let say the Mean operator) is a linear operator with respect to random variables.
However, I don't want to particularize my demonstration by using this or that statistical distribution but simply the notion of random variable.
I have therefore created a specific Distribution named  MinimalAbstractDistribution in which only the mean and variance are defined.

When Statistics:-Mean is applied to the expression (A*p+q) where p and q are names and A is a random variable with distribution MinimalAbstractDistribution, linearity is effectively used.
But not when it is applied to A/p or A-q.

Why that?
Is there a way of defining a statistical distribution so that Mean behaves as expected?

(You will easily understand that no workaround of the form

```Mean(A+q);
eval(%, q=-q);

# or
```

can be accepted in a lesson).

 > restart
 > with(Statistics):

 > MinimalAbstractDistribution := proc(i)   Distribution(Mean=mu[i], Variance=sigma[i]^2) end proc:
 > A := RandomVariable(MinimalAbstractDistribution(1))
 (1)
 > [Mean, Variance](A);
 (2)
 > Mean(p*A+q); Mean(p*(A+q))
 (3)
 > # But Mean(A-q); Mean(A/p)
 (4)