@Nicole Sharp I kept 2015 as it is an institutional licence that my students had access to. But 2022 and 2023 were just licenced to me, and I kept 2022 when I updated to 2023 "just in case". Now I have updated to 2024 on a different computer and will soon junk the old computer and all three earlier versions. Decreases in capability are very rare. I don't know anything about Quandl, but it seems the DataSets package has just changed so similar data is now built-in to Maple, so there is perhaps not much decrease in capability?

In general, there is no problem having multiple versions - I have a windows 10 system with 2015, 2022 and 2023 happily coexisting.

@one man With apologies to Rouben, I hacked his code to get the arclength, which for his solution agrees approximately with your second solution. Is your first one just symmetrically equivalent with not very accurate arclength? It might be possible to get such solutions from Rouben's code by givng dsolve an approximate initial solution.

geodesic-on-rounded-cube-arclength.mw

On Maple 2023, if I have a worksheet open I see Sign in at the top right corner. I sign in and on the sign-in window there is a "Remember me" check box. If I check this, then I am persistently signed in; my avatar shows when I open a new worksheet. So perhaps it is some sort of access/permissions issue on your computer. (I don't have Maple 2024 at my location right now.)

@zenterix I think @C_R has the solution for the g=1 case, which was just your test case. For the physically realistic case of g>1, it can be done via the symbolic solution. But for numerical integration I think it has to be non-dimensionalized along @C_R's lines ,since V^g is problematic with g=1.1 - see end of worksheet.

Edit: updated to correct incorrect assumption about temperature

adiabatic.mw

Edit: like many derivations the derivation of P*V^g = k involved raising something with units to a non integral power, which is the root cause of the problem here. So probably the derivation can be improved by adding some variables that are just there to cancel the units, e.g., (V/V0)^g with V0 = 1 m^3, similar to @C_R's treatment . But then of course V0 will pop up somewhere else in k.

@salim-barzani OK, I think I understand. 

same_equation_different_parameter2.mw

@Scot Gould Yes, I find this sort of thing frustrating and have to rediscover it frequently when I want an unsual data structure. I think as a rule, Arrays are more permissive about what you put into them, but for Matrices and Vectors, elements that are Vectors/Matrices/lists get incorporated into a single Matrix/Vector of numbers/symbols.

In Maple 2024, I get a warning "Warning, units problem, not enough information to unambiguously deduce the units of the variables {V, n}; proceeding as if dimensionless"

in the integration limits you have n times a unit being a volume, which seems strange. Do you mean something like V = n*V1..m*V1 where n is dimensionless and V1 is a volume. Or did you mean n and m to have values before the integral? 

plot3d(-x^2/9 + y^2/4, x = -5 .. 5, y = -5 .. 5)

Do you mean surface? Do you want the shortest path on the surface?

@salim-barzani I believe you forgot to apply the chain rule in the part you did by hand. Here is a corrected version that verifies with pdetest on the original equation.

f12.mw

@dharr I am trying to understand how you get from the pde to the ode. I can't get Maple to do this so I am wondering if there is some hidden assumption here that needs to be specified. If so, that may be why pdetest fails. Or the solution may not be correct.

pde-solve2.mw

As others have already asked you to before, please upload your actual worksheet using the green up-arrow in the Mapleprimes editor (not just an image.) That way, we don't have to retype your input, and you may get a better response.

@mmcdara Nice analysis. Vote up. No, I don't have the GlobalOptimization toolbox.

@Ariathm It might be finding the wrong local minimum. In non-linear least square problems like this getting the initial guess values close to the right answer is key to success, and I might have chosen some bad values.

I noticed p__eng is strangely like p__3 but not quite. Perhaps it is better to calculate these in Maple from some earlier expression, rather than enter them by hand. Especially if you have some form without the fractional powers, it will help.

@dharr The long calculation has probably to do with the difficulty of finding derivatives for the horrible expression. The following simplifies the expression enough that it proceeds to a solution. I used simplify(..,symbolic) to get rid of the fractional powers. In principle that can give invalid results, but here I think it is probably OK since everything is positive, but you should check that the answer makes sense. Note that the kappa value found is at the end of the range.

test2.mw

Looks OK, given that kappa is not correct yet

test3.mw