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Question: why Maple symgen does not find this symmetry?

Question:why Maple symgen does not find this symmetry?

nm 10748 Maple 2024
ode detools differential-equations symgen
February 10 2025
3

page 37 of book Symmetry Methods for Differential Equations by Hydon gives this example

When I wanted to verify it using Maple., symgen did not find these symmetries. Only when I give it using HINT the exact form it find them.  


 

> 

interface(version);

`Standard Worksheet Interface, Maple 2024.2, Windows 10, October 29 2024 Build ID 1872373`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1843 and is the same as the version installed in this computer, created 2025, January 25, 22:5 hours Pacific Time.`

> 

libname;

"C:\Users\Owner\maple\toolbox\2024\Physics Updates\lib", "C:\Program Files\Maple 2024\lib"

> 

restart;
> 

ode:=diff(y(x),x) = (y(x)^3+y(x)-3*x^2*y(x))/(3*x*y(x)^2+x-x^3)

diff(y(x), x) = (y(x)^3+y(x)-3*x^2*y(x))/(3*x*y(x)^2+x-x^3)

> 

the_syms:=DEtools:-symgen(ode)

> 

the_syms:=DEtools:-symgen(ode,'way'='all')

> 

the_syms:=DEtools:-symgen(ode,'way'='formal')

> 

#only when I give it the exact general form, it finds them !
the_syms:=DEtools:-symgen(ode,'HINT'=[a*y^3+b*y-c*x^2*y,d*x^3-e*x-f*x*y^2])

[_xi = -3*x^2*y+y^3+y, _eta = x*(x^2-3*y^2-1)]

> 

 


 

Download why_no_syms_feb_10_2025.mw

Is this expected? Should it not have found them on its own?

Is it possible Maple internally does not automatically try Ansatz  of polynomials higher than quadratic to keep computation time low?   If so, I wonder if there is a way to tell it to try cubic or higher orders (like tryhard) option but for symgen?  I will search help more to see if there is a way to do this...
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