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Alfred_F

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These are questions asked by Alfred_F

identify a float...

Alfred_F 465 Maple 2024
integration identify
February 13 2026
1 2

In the attached file, I want to calculate the integral Q1. Numerically, this is easy to do in Maple. For theoretical reasons, the exact result pi/e is known. However, a contradiction arises between command lines (4) and (5). Command (6) is also unsuccessful, as its exact result is unknown. What am I doing wrong?

restart

Q1 := int(sin(Pi*x)/(x^x*(1-x)^(1-x)), x = 0 .. 1)

int(sin(Pi*x)/(x^x*(1-x)^(1-x)), x = 0 .. 1)

 (1)

evalf[100](Q1)

1.155727349790921717910093183312696299120851023164415820499706535327288631840916939440188434235673559

 (2)
> 

evalf[100](Pi/exp(1))

1.155727349790921717910093183312696299120851023164415820499706535327288631840916939440188434235673559

 (3)
> 

is(Q1 = Pi/exp(1))

false

 (4)
> 

identify(evalf[100](Q1))

Pi*exp(-1)

 (5)

identify(.2340257795502385151002175791580229871350403567739388325733228478980460706709848394726222465477567339)

.2340257795502385151002175791580229871350403567739388325733228478980460706709848394726222465477567339

 (6)

NULL

Download test.mw

2D Math editing behavior...

Alfred_F 465 Maple 2024
2dmath gui editing
February 11 2026
1 1

The plot in the attached file only works if the complete function expression is entered. If only the function name is entered, no plot appears. What am I doing wrong?test.mw

restart;

c(x)dsum(sin(10^k*x)/10^k, k = 1 .. 10^2)

plot(c(x), x = -(1/4)*Pi .. (1/4)*Pi)

  

``

c(x)dsum(sin(10^k*x)/10^k, k = 1 .. 10^2)

plot(sum(sin(10^k*x)/10^k, k = 1 .. 10^2), x = -(1/4)*Pi .. (1/4)*Pi)

  

 

NULL

Download test.mw

General solution sought...

Alfred_F 465 Maple 2024
ode dsolve differential-equations
January 16 2026
0 1

I'm looking for the general solution to the attached differential equation. Maple doesn't provide it. What am I doing wrong?

restart

ode5 := diff(y(x), x) = (8*y(x)*b-32*b^2*x/y(x)-64*b^2*x^2*y(x))/(3*y(x)^2+8*b*x-16*b^2*x^2/y(x)^2)

diff(y(x), x) = (8*y(x)*b-32*b^2*x/y(x)-64*b^2*x^2*y(x))/(3*y(x)^2+8*b*x-16*b^2*x^2/y(x)^2)

 (1)

simplify(ode5)

diff(y(x), x) = ((64*b^2*x^2-8*b)*y(x)^3+32*b^2*x*y(x))/(-3*y(x)^4-8*b*x*y(x)^2+16*b^2*x^2)

 (2)

dsolve(ode5, y(x))

NULLNULL

Download testdgl5.mw

Conversion of a term...

Alfred_F 465 Maple
syntax expand simplification
December 28 2025
1 6

In the attached file, I want to transform (1) into (3) and back again (3) into (1). Attempts using CompleteSquare and expand in combination with other commands have failed. I would appreciate any advice.

dio1.mw

Lipschitz condition...

Alfred_F 465 Maple
ode differential-equations
December 13 2025
2 2

I recently read something in another forum about solving a simple ordinary differential equation as an initial value problem (file attached). An unexpected solution behavior was interpreted there as a weakness of the software. However, upon closer inspection, the cause is different, and as a software novice, I cannot determine it myself.

Therefore, my question is:

Is there a way, using Maple, to check the Lipschitz condition in the neighborhood of the initial value before starting the solution of an explicit first-order system of differential equations as an initial value problem?

DGL_test.mw

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