Although this equation can be solved analytically, it is rather cumbersome.

This is one of the few cases where the Schrödinger equation can be solved analytically.

Some of the simplest reactive transport problems can be solved analytically.

Such systems may be solved analytically, for this case by integrating:

Dynamical systems describing some types of the clusters can be solved analytically.

Simple two-body problems, for example, can be solved analytically.

The equations of motion in general relativity are notoriously hard to solve analytically.

The advantage of this description is that it gives important insight about the dynamics, even if the initial value problem can not be solved analytically.

The method is useful for obtaining numerical solutions to problems too complicated to solve analytically.

Many differential equations cannot be solved analytically, in which case we have to satisfy ourselves with an approximation to the solution.