MaplePrimes - Newest Questions

Should dsolve return this?

nm — Wed, 17 Jun 2026 04:31:03 Z

given

ode:=2*x^(1/2)*diff(y(x),x)-y(x) = -sin(x^(1/2))-cos(x^(1/2)); 
ic:=y(infinity) = y__0; 
sol:=dsolve([ode,ic]);

It gives

This solution satisfies the ode itself. Now cos(sqrt(x)) when x=infinity is -1..+1

But IC says y(infinity)=y0 so odetest do not verify the IC and gives this

odetest(sol,[ode,ic]);

I think dsolve should not have returned a solution at all.

What do the experts here think of this result?

Maple 2026.1 on windows 10

Check procedure existance

Anthrazit — Tue, 16 Jun 2026 20:19:49 Z

I'm trying to rewrite my initialization routines a bit, and want to find out if there are any other procedures with a certain name that should be called.
However there seems to be a problem with the scope. I'm trying to explain that with a little program.

The question is - why is InitSpecific not found by the InitCommon procedure here?

Download InitCommon.mw

Animating the Dzhanibekov effect?

Earl — Tue, 16 Jun 2026 18:40:37 Z

The uploaded worksheet references two youtube videos.

The first one displays the animation of a simple device rotating about an axis tilted at a small angle from the device's principal axis having an intermediate moment of inertia.

The animation and accompanying verbal description demonstrate the Dzhanibekov effect.
The second video contains the first video's narrator's equations which produce the values used in creating the animation.

The uploaded worksheet contains my failed attempt to reproduce these values.

Please suggest the Maple 2020 compatible statements which correctly produce these values.

Dzhanibekov_effect.mw

evala,Sqrfree output

C_R — Tue, 16 Jun 2026 16:10:35 Z

I am new to evala (and the math behind).

On ?evala,Sqrfree at the first bullet point I was wondering if there isn't a "u" missing here

Can someone confirm?

How does this divergent series get evaluated?

Angelo Melino — Mon, 15 Jun 2026 19:12:19 Z

I asked an LLM to provide an expansion of the MacDonald function of arbitrary order (a modified Bessel function of the second kind with purely imaginary order and positive argument), K(I*y,r), as a weighted sum of MacDonald functions of integer order. It came back with

K(I*y,z)=2*sinh(Pi*y)/Pi* [K(0,r)/2*y+sum( (-1)^n*y*BesselK(0,r)/(y^2+n^2),n=1..infinity)]

(see below for more readable text)

I evaluated the LHS and RHS using Maple 2026 for various choices of y and r and found numerical agreement using both "sum" and "Sum". I was very pleased until I realized that the RHS isn't a convergent series!

Can anyone explain to me how Maple pulls this off!

(I asked Maplesoft Tech Support but they said it is above their pay grade... I suspect that Maple is using Borel summability to evaluate the RHS but I haven't been able to verify that)

I apologize, but I can't see how to attach a .mw file, so I've cut and pasted the code below

why not to collect R(xi) accurately

bashar27 — Mon, 15 Jun 2026 08:21:07 Z

restart;

T := R(xi)*R(xi) + lambda;

u := A[0] + A[1]*R(xi) + B[1]/R(xi);

d[1] := A[1]*T - B[1]*T/R(xi)^2;

d[2] := 2*A[1]*R(xi)*T - 2*B[1]*T/R(xi) + 2*B[1]*(R(xi)^2 + lambda)*T/R(xi)^3;

expand(((-alpha^2*b^2 + a^2)*alpha^2)/(2*beta)*d[2] + (omega + alpha^2*(alpha^2*l^2 + k^2)/2 - a*C[1]/(-alpha^2*b^2 + a^2))*u[0]/(beta - 2*beta*a^2/(-alpha^2*b^2 + a^2)) + u[0]*u[0]*u[0]);

value(%);

simplify(%);

collect(%, R(xi));

/ 6 4 4 2\ 3
A[1] \-alpha b + a alpha / R(xi)
------------------------------------
/ 2 2 2\
beta \alpha b + a /

/ 6 4 4 2\
A[1] lambda \-alpha b + a alpha / R(xi)
+ ------------------------------------------ +
/ 2 2 2\
beta \alpha b + a /

/ /
1 |/ B[1] \ |
--------------------- ||A[0] + A[1] R(xi) + -----|[0] |beta
/ 2 2 2\ \\ R(xi)/ \
beta \alpha b + a /

2
/ 2 2 2\ / B[1] \
\alpha b + a / |A[0] + A[1] R(xi) + -----|[0]
\ R(xi)/

1 2 2 6 1 / 2 2 2 2\ 4
+ - b l alpha + - \-a l + b k / alpha
2 2

\\
/ 1 2 2 2 \ 2 2 ||
+ |- - a k + b omega| alpha - a omega + a C[1]||
\ 2 / //

/ 6 4 4 2\
B[1] lambda \-alpha b + a alpha /
+ ------------------------------------
/ 2 2 2\
beta \alpha b + a / R(xi)

6 4 2 4 2 2
-alpha b lambda B[1] + a alpha lambda B[1]
+ ------------------------------------------------
/ 2 2 2\ 3
beta \alpha b + a / R(xi)