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Suggestions in Differential Equations

   Suggestions are inspirations based on similarities. They are an indispensible part of mathematical thinking. They are neither formal arguments nor results derived from quoting theorems. We may provide reasons to support them but not proofs.
  1. [Cod, p.139, (1.7)] is suggested by the the variation-of-constants formula, but is not derived from it because jis unknown. We may use either (e-it, eit) or (eit, e-it) as the first row of F(t) in [Cod, p.75, (3.2)], but only the former choice may lead to [Cod, p.139, (1.7)].

  2. [Cod, p.139, (1.4)] is suggested by [Cod, p.89, (6.29); p.133, l.6].