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Question: symgen hangs on formal algo on first order ODE

Question:symgen hangs on formal algo on first order ODE

nm 8552 Maple 2020
detools symgen
September 05 2020
2

Any idea why symgen hangs when using formal algorithm on this first order ode? I was just comparing the Lie symmetries generated for this ode using different algorithms when I noticed this hang on formal.

The textbook gives this result btw

From help on symgen it says

The first algorithms, called formal, formulates a linear PDE system for the infinitesimals [xi, eta], then formally triangularize this system - using differential algebra techniques - finally tacking the resulting uncoupled system. When successful, this algorithm returns the complete set of point symmetries admitted by a given ODE of order 2 or higher. NOTE: this algorithm is advantageous mainly for 2nd and higher order ODEs. The algorithm works as well in the case of first order ODEs, but in this case the subproblems it will need to solve to find the symmetries are as difficult to solve as the first order ODE itself.
 

But on Maple 2020.1 server seems to hang, taking 100% CPU. I had to terminate mserver.exe manually since clicking on interreupt button from worksheet has no effect. This only happens with formal algoritm. All others work very fast. 

I know help says this is meant for second order ODE's, but it also says it works  well for first order.  It seems to be stuck in solve call somewhere. Is this to be expected sometimes when using formal algo in symgen for first order ode's?

Maple can solve the ODE very quickly otherwise.


The following ode also hangs in symgen

ode:=diff(y(x),x)=x*y(x)^2-2*y(x)/x-1/x^3;


 

> 

restart;
> 

interface(version)

`Standard Worksheet Interface, Maple 2020.1, Windows 10, July 30 2020 Build ID 1482634`

> 

Physics:-Version()

`The "Physics Updates" version in the MapleCloud is 794 and is the same as the version installed in this computer, created 2020, September 3, 23:37 hours Pacific Time.`

> 

#hangs on formal, why?
restart;
ode:=diff(y(x),x)=(y(x)-4*x*y(x)^2-16*x^3)/(y(x)^3+4*x^2*y(x)+x);
DEtools:-symgen(ode,y(x),way=formal)

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

> 

restart;
ode:=diff(y(x),x)=(y(x)-4*x*y(x)^2-16*x^3)/(y(x)^3+4*x^2*y(x)+x);
sol:=dsolve(ode,implicit)

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

(1/2)*y(x)^2+(1/2)*arctan((1/2)*y(x)/x)+2*x^2-_C1 = 0

> 

 


 

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