Eight Perspectives on the Exponentially Ill-Conditioned Equation εy" - xy' + y = 0*.

Boundary-value problems involving the linear differential equation εy" - xy' + y = 0 have surprising properties as ε → 0. We examine this equation from eight points of view, showing how it sheds light on aspects of numerical analysis (backward error analysis and illconditioning), asymptotics (boundary layer analysis), dynamical systems (slow manifolds), ODE theory (Sturm--Liouville operators), spectral theory (eigenvalues and pseudospectra), sensitivity analysis (adjoints and SVD), physics (ghost solutions), and PDE theory (Lewy nonexistence). [ABSTRACT FROM AUTHOR]