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Question: using hint for symgen, why not giving answer here?

Question:using hint for symgen, why not giving answer here?

nm 8552 Maple 2020
detools symgen
September 07 2020
3

When I give symgen a HINT, using functional form f(x),g(x)*y it does not generate the infinitesimals of the Lie group for this ODE.

But from the answer given using way=abaco1 it is clear they have this form, where f(x)=-1/x and g(x)=1/x^2

From help, it says

HINT=[e1,e2], indicates to the solver that it should take e1 and e2 as the infinitesimals, where e1 and e2 can contain a maximum of two indeterminate functions. The solver tries to determine the infinitesimals to solve the problem.

And I am using only two indeterminate functions. These are f(x) and g(x)

Am I making a mistake somewhere? Please see worksheet below.


 

> 

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 801 and is the same as the version installed in this computer, created 2020, September 7, 14:32 hours Pacific Time.`

> 

restart;
ode:=diff(y(x),x)=(1-y(x)^2)/(x*y(x))+1;
#why this below do not give result?
DEtools:-symgen(ode,HINT=[f(x),g(x)*y]);

diff(y(x), x) = (1-y(x)^2)/(x*y(x))+1

> 

DEtools:-symgen(ode,way=abaco1);

[_xi = -1/x, _eta = y/x^2]

> 

#it works for this though. May be the two functions
#can  not be both functions of x at same time?
#one function must be function of x and the other of y?
#But help does not say that.

ode :=diff(y(x),x)=(x+cos(exp(-x)*(1+x)+exp(y(x))))/(exp(x+y(x)));
DEtools:-symgen(ode,HINT=[f(x),x*g(y)]);

diff(y(x), x) = (x+cos(exp(-x)*(1+x)+exp(y(x))))/exp(x+y(x))

[_xi = exp(x), _eta = x*exp(-y)]

> 

 


 

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