>>13463490If you are concerned about fine mathematical details (for use in a formal proof), the analytical solution might be required.
Even in proofs, usually an approximation (with error bounds) is used because it is easier (or simply possible) to work with.
Most of the time (real world applications), the approximate solution is good enough.
Even if you have an analytic solution, you end up using approximations in practice through truncated infinite series and finite precision of computers.
