In this addendum-like text with just two references, an alternative, graphical-method-inspired constructive re-derivation of some of the results of paper [2] is offered. Although the subject itself (viz., the nonlinear Cauchy problem $y'(x) = cos[\pi xy(x)]$) carries multiple apparently remarkable features (see also extended abstract MR3216779), calling it (in a way inspired by some parallels with certain elementary quantum systems) a ``nonlinear eigenvalue problem'' seems exaggerated. A title like ``ordinary differential equations with separatrices'' would probably fit the subject better. MR3254850 (Sent 2014-12-10) Kerr, Oliver S. Comment on `Nonlinear eigenvalue problems'. J. Phys. A 47 (2014), no. 36, 368001, 5 pp. 34A12 (34C15 34D05 34E20 34M55 37K10) .