I lost (probably deleted..) the context for this question, but I believe
the distinction that was being made was between a numerical solution
(e.g. as a sequence of numbers, or maybe an approximate interpolating
polynomial) and a solution in the form of a formula (analytic). Now there
may be formulas that are not analytic in the Cauchy-Riemann sense
that could come up somehow.
I don't know if the code that you are generating and timing for
Maxima was run through the compiler; perhaps it is irrelevant if you
are using bigfloats. But if simple machine floats can work,
proper compiling might get a factor of 30 speedup.
RJF