@sand15 

Thanks, that looks great in the maplet plot.
In Maple 2025, the explorer plot is larger for the plot3d structure size = [1100, 850] , so it's also a good plot.
I don't know how difficult it is to create an explorer plot or a maplet in comparison.

Creating maplets with AI did not prove successful (not with deepseek: goes very well), but that may also have to do with the fact that I have to give step-by-step instructions. But then I have to delve into the maplet code again.
You start with a blank screen and then fill in the components.
There should also be a maplet version created by you on the forum, but I can't see it?

Note: using a 10-year-old version of Maple means you're lagging behind in terms of the new possibilities

uitleegoop_prammering_3_voorbeelden_vergelijk_mprimes_20-10-2025.mw

@nm 

it was wrong about the manual as it seems,unfortunaly. 

version 3 seems to be right oop programming, ?

@sand15 
Yes, you could also enlarge the plot and then you would definitely see it. C(t,0) surface, I suppose.
Otherexample pde
exploreplotgebruiken_met_pdes_mprimes_13-10-2025.mw

SOLUTION SURFACE OF PARTIAL DIFFERENTIAL EQUATION

SOLUTION_SURFACE_OF_PARTIAL_DIFFERENTIAL_EQUATION_mprimes_12-10-2025DEF.mw

@sand15 

Thank you. It is indeed not a question, but more of a small investigation into how to deal with a PDE.

Now only for u(x,t) solutions surfaces

The plot legend now attached makes it much clearer, because the start for this PDE solution is when C(t) = 0 is an initial surface, but I do not see this initial surface in the plot?

An Explore plot would also be a good idea to see the solution surfaces for different boundary conditions.

@Rouben Rostamian  

It's all done via AI, because I'm not a experienced Maple user, as I don't have the knowledge at my fingertips at the moment.

PlotCilinderInBol(0., 1, true)

Rotating spherical surface  containing a moving cylinder 
The cylinder diameter can be adjusted and the animation can be turned on or off.

bol_en_cilinder_animatie_mprimes_10-10-2025.mw

@Rouben Rostamian  
I do nothing with transparency.
The second new code does not affect transparency, but simply draws now a hole in the spherical surface.

For a surface other than a sphere, you could determine the 3D intersection curve, turn it into a white surface, and position it.

animatie_halve_bol_met_cilinder_mprimes_recreatief_9-10-2025.mw

@salim-barzani 
t_plot_domein_definition_for_functie_K_mprimes_8-10-2025.mw

@sand15 
Thanks for the oversight of this subject.

BesselI and BesselK are the modified Bessel functions of the first and second kinds, respectively.  They satisfy the modified Bessel equation:
            "x^2*`y''` + x*`y'` - (v^2 + x^2)*y = 0"
Seems that here is no explicit third kind modified bessel function in Maple ?

There is a singularity at (0,0)  ?

@Kitonum 
Thanks 

with(Optimization);
[ImportMPS, Interactive, LPSolve, LSSolve, Maximize, Minimize, 

  NLPSolve, QPSolve]

Minimize(419*x^2 + 116*x*y - 426*x*z + 78*y^2 - 142*y*z + 133*z^2 - 1604*x - 682*y + 1086*z + 2306);
       [0., [x = 7.00000000000007, y = 11.0000000000001, 

         z = 13.0000000000002]]

Seems to be not strict symbolic ?

@salim-barzani 
Is this function for the 3 plots on different times ?
"can you plot by Ai you have lets see how many shape you have ?"   what are shapes ?

2*((t*(-alpha*conjugate(lambda[1] + lambda[2]*I)^3 + b*conjugate(lambda[1] + lambda[2]*I) + c*r[2] + a) + 2*beta*(y*conjugate(lambda[1] + lambda[2]*I) + z*r[2] + x))/(2*beta) + (t*(-alpha*(lambda[1] + lambda[2]*I)^3 + b*(lambda[1] + lambda[2]*I) + c*r[1] + a) + 2*beta*(y*(lambda[1] + lambda[2]*I) + z*r[1] + x))/(2*beta))/(((t*(-alpha*(lambda[1] + lambda[2]*I)^3 + b*(lambda[1] + lambda[2]*I) + c*r[1] + a) + 2*beta*(y*(lambda[1] + lambda[2]*I) + z*r[1] + x))*(t*(-alpha*conjugate(lambda[1] + lambda[2]*I)^3 + b*conjugate(lambda[1] + lambda[2]*I) + c*r[2] + a) + 2*beta*(y*conjugate(lambda[1] + lambda[2]*I) + z*r[2] + x)))/(4*beta^2) - 4/((lambda[1] + lambda[2]*I - conjugate(lambda[1] + lambda[2]*I))^2*alpha))

@salim-barzani 

That resembles a normal 3D plot at u= 0 , where you see peaks and a density plot at level -1.

Is that possible?