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

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

Maple 2020

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)

 > Physics:-Version()

 > 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]);

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

 > #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)]);

 >