Is there a mathematical reason why Maple does not allow expansion point for solving an ode using series solution to be different than where initial conditions are located?

I do not see why this restriction is there. Here is first order ode, where expansion point is x=1 and initial condiitons are also at x=1

restart;
ode:=diff(y(x),x)=x^3;
dsolve([ode,y(1)=1],y(x),'series',x=1)

            y(x) = (1 + (x - 1)) + 3/2*(x - 1)^2 + (x - 1)^3 + 1/4*(x - 1)^4 + O((x - 1)^6)

No problem. But when expansion point at x=0, it complains

restart;
ode:=diff(y(x),x)=x^3;
dsolve([ode,y(1)=1],y(x),'series',x=0)

Error, (in dsolve/SERIES) conflicting specifications of the series expansion point: 1 v.s. 0

I know help mentions that it uses initial conditions point for expansion if given, and if no IC is given, then it uses x=point if given and if no x=point is given then it default to x=0.

But my question is, why it does not handle the case when the expansion point is given explicitly and is at a different location than where IC are given? Is this simply just a feature missing that could be added in a future release if needed, or is it due to some mathematical reason that I do not see?

I would have expected it to first find the series solution around the given expansion point, then use the IC to determine the unknown constant after that, just like we normally do when solving an ode using standard methods not using series expansion.

I am using Maple 2023

S := t -> tanh(ln(1 + t^2))

diff(S(t), t $ n)=1/GAMMA(1-n)-1/4*pochhammer(-n,n)*Sum(_alpha^3*(t-_alpha)^(-1-n),_alpha =RootOf(_Z^4+2*_Z^2+2))

why the root of? its easy to see the roots are given by

solve(_Z^4 + 2*_Z^2 + 2 = 0);

(-1-I)^(1/2), -(-1-I)^(1/2), (-1+I)^(1/2), -(-1+I)^(1/2)

its equivalent to the roots of (z^2 + 1)^2 + 1

it seems very weird that maple stops here rather than turning it into a 4-element array

I read the article "ONEOptimal: A Maple Package for Generating One-Dimensional Optimal System of Finite Dimensional Lie Algebra", and also searched out in Maplesoft website, but couldn't found. Does anyone have the package?

I am trying to see if there is a way to submit maple code as a worksheet and get results back as worksheets in a cluster. 

if i solved two integral seperately..it solved.. but i can't solve together..what's wrong...please help

Download 2.mw

i want to sovle this problem ..but i dont' know how to start..please help me.how to solve this eqution?

Download 1.mw

Is it possible to read in specific parts of a bmp image? 

TODAY I GOT AN INSPIRATION TO CREATE 3D GRAPH EQUATION OF WALKING ROBOT (ED-209) IN CARTESIAN SPACE USING ONLY WITH SINGLE IMPLICIT EQUATION.

ENJOY...

How to Create Graph Equation of Wankel Engine on Cartesian Plane using Single Implicit Function run by Maple Software

Enjoy...

what is the homology matrix that plates the ABCE square on the NPCM square
I think it may bi find out with the rotation angle, the vector of translation and the homothety ratio.
restart;  
with(geometry):  
with(plots):  
_EnvHorizontalName = 'x':  _EnvVerticalName = 'y':

point(A, 0, 1):
point(B, 1, 1):
point(C, 1, 0):
point(E, 0, 0):
square(Sq, [A, B, C, E]):
Phi := (1 + sqrt(5))/2:
point(N, (2 - Phi)/(Phi - 1), 1):
line(BE, [B, E]):
MakeSquare(s1, [N, C, 'diagonal']):
point(M, (3 - sqrt(5))/(2*sqrt(5) - 2), (3 - sqrt(5))/(2*sqrt(5) - 2)):
point(P, (1 + sqrt(5))/(2*sqrt(5) - 2), (3*sqrt(5) - 5)/(2*sqrt(5) - 2)):
T:=<simplify(coordinates(midpoint(O1,E,B))-coordinates(midpoint(O2,M,P)))>:
simplify(distance(O1,O2)):
line(MN,[M,N]):eq:=Equation(%,[x,y]):sol:=solve(eq,y):
Ang:=Pi/2-arctan(diff(sol,x)):
r:=simplify(distance(N,M)):
line(MP,[M,P]):eq:=Equation(%,[x,y]):subs(y=0,%):point(Q,solve(%,x),0):
line(PQ,[P,Q]):
homology(Sq1, Sq, C, Ang, 'clockwise', r):

display(draw([A(color = black, symbol = solidcircle, symbolsize = 12), 
B(color = black, symbol = solidcircle, symbolsize = 12), 
C(color = black, symbol = solidcircle, symbolsize = 12), 
E(color = black, symbol = solidcircle, symbolsize = 12), 
N(color = black, symbol = solidcircle, symbolsize = 12), 
Sq(color = red, filled = true, transparency = 0.9), 
BE(color = green), 
PQ(color = black),
 Sq1(color = black), 
s1(color = red, filled = true, transparency = 0.8)]), 
textplot([[coordinates(A)[], "A"], 
[coordinates(B)[], "B"], 
[coordinates(E)[], "E"], 
[coordinates(N)[], "N"], 
[coordinates(P)[], "P"], 
[coordinates(M)[], "M"], 
[coordinates(Q)[], "Q"], 
[coordinates(C)[], "C"]], 
align = [above, right]), view = [-0.6 .. 1.5, 0 .. 1], axes = none);
 

Given a constant gamma, gaussian random variables S[1] and S[2], and a linear combination of gaussian random variables Omega, I need to compute Exp[ Omega | S[1], S[2] ] - (gamma/2)*Var[ Omega | S[1], S[2] ]. I am not experienced in Maple. In the attached script I include many step-by-step details on what I need to do, as well as some notes where I get stuck:

150423_OptimizationProblem.mw

It would be convenient if you could directly fix this and share the working version. Thanks!

The conditional means and variance terms are calculated according to the 2D version of the script 3_gaussian_mmcdara.mw provided by @mmcdara.

Here is a string, and I want to treat consecutive single digits as a single number and extract them. I can process it using regular expressions in Python. I'm not sure if Maple can handle it in a similar way.

import re
sstr1 = "124e34e243e45e56e76f34e45e23ea12e98e34e43"
num=re.findall(r'\d+', sstr1)
s=list(map(int, num))
print(s)

[124, 34, 243, 45, 56, 76, 34, 45, 23, 12, 98, 34, 43]

Is there an equivalent regular expression method in Maple?

As usual, I have a tricky question. There is an integral that Maple can take numerically

R0 := 1/(a-sqrt(b+c*cos(x)));

Now let's put the coefficients, e.g.

 a := 0.9; b := 4.5; c :=0.1

and take the integral from 0 to 2*Pi

R1 := evalf(int(R0, x = 0 .. 2*Pi));

Also, there is an exact analytical result that Maple gives (I give it after simplifying it to avoid division by zero for the limit x=0 and x=2*Pi)

R2:=-4*((a^2-b+c)*EllipticK(sqrt(-2*c/(b-c)))-a^2*EllipticPi(2*c/(a^2-b+c), sqrt(-2*c/(b-c))))/((a^2-b+c)*sqrt(b-c));

As it turns out, the results are completely different. In the first case -5.145818656, while for the second case -3.612771378+0.I

Moreover, If we change the coefficients to a := 0.9; b := 4.5; c := -4 then I obtain Float(undefined)+3.662506136*I and -2.362349457+3.662506117*I , respectively.

My question: how to avoid this descepancy?

A := Matrix([[1, 3, 9, 2, 3, 7, 1, 1, 5, 4, 7], [7, 5, 5, 4, 9, 3, 4, 5, 3, 5, 3], [5, 2, 1, 6, 5, 4, 2, 9, 6, 6, 6], [2, 4, 1, 9, 5, 1, 1, 2, 1, 1, 7], [1, 9, 2, 3, 2, 9, 8, 2, 2, 7, 3], [5, 5, 3, 7, 2, 1, 5, 2, 7, 8, 3], [2, 2, 1, 7, 8, 7, 8, 2, 1, 4, 5], [8, 9, 6, 4, 9, 4, 1, 5, 4, 2, 5], [5, 7, 4, 5, 3, 2, 8, 3, 6, 2, 6], [6, 7, 8, 9, 9, 9, 8, 4, 8, 9, 3]]);

Use Maple to create the vector b that is column 2 from A and the matrix C that is made from columns 1 to 1 and 3 to 11 of A (in the same order as the columns of A.

Now solve the matrix equation

Cx=b

and enter the 4^th component of the unique vector solution for x in the box below.