  We revisit a textbook example of a singularly perturbed nonlinear
boundary-value problem. Unexpectedly, it shows a wealth of phenomena that seem
to have been overlooked previously, including a pitchfork bifurcation in the
number of solutions as one varies the small parameter, and transcendentally
small terms in the initial conditions that can be calculated by elementary
means. Based on our own classroom experience, we believe this problem could
provide an enjoyable workout for students in courses on perturbation methods,
applied dynamical systems, or numerical analysis.
