How to define a generic function of two variable t and r

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Like this:

sage: f(t,r) = function('f')(t, r)

Then f stands for the function (technically a callable symbolic expression):

sage: f
(t, r) |--> f(t, r)

and f(t,r) stands for the symbolic expression expressing f acting on (t,r):

sage: diff(r^3*f(t,r), r)
r^3*diff(f(t, r), r) + 3*r^2*f(t, r)