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Without some sample problem code, it is not easy to come up with sample solution code. So let's pontify...

You can extract the variables of a symbolic expression with the method .variables() ; this returns a tuple, which you can turn in a set thanks to the function set. Its difference() method allows you to substract the original parameters (present in the suystem before solution) ; what remains are the new parameters introduced by the solver.

What remains to do is to map such a function to the elements of the solution(s) and compute the union of the result.

Made-up example for an ordinary differential equation :

sage: Ovars=var("t, a, b, c")
sage: f=function("f")
sage: de=a*f(t).diff(t,2)+b*f(t).diff(t)+c==0
sage: with assuming(b!=0):Sol=desolve(de, f(t), ivar=t) ; Sol
_K2*e^(-b*t/a) + _K1 - (b*c*t - a*c)/b^2
sage: len(Params:=set(Sol.variables())-set(Ovars))
2
sage: Params
{_K2, _K1}

Extrapolate for multiple-elements solution(s) and/or multiple solutions, and season to teaste. Serve cool...

HTH,

Without some sample problem code, it is not easy to come up with sample solution code. So let's pontify...

You can extract the variables of a symbolic expression with the method .variables() ; this returns a tuple, which you can turn in a set thanks to the function set. Its difference() method allows you to substract the original parameters (present in the suystem before solution) ; what remains are the new parameters introduced by the solver.

What remains to do is to map such a function to the elements of the solution(s) and compute the union of the result.

Made-up example for an ordinary differential equation :

sage: Ovars=var("t, a, b, c")
sage: f=function("f")
sage: de=a*f(t).diff(t,2)+b*f(t).diff(t)+c==0
sage: with assuming(b!=0):Sol=desolve(de, f(t), ivar=t) ; Sol
_K2*e^(-b*t/a) + _K1 - (b*c*t - a*c)/b^2
sage: len(Params:=set(Sol.variables())-set(Ovars))
2
sage: Params
{_K2, _K1}

Extrapolate for multiple-elements solution(s) and/or multiple solutions, and season to teaste. taste. Serve cool...

HTH,