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I Wonder How the Ditch Has Become So Clear (2/23/2009)

Prologue. The constant O in [Cod, p.158, (4.41)] depends on m. By mistake, somehow I thought I needed to prove that the constant O is independent of m. Being stuck in the middle of a long proof after many failed attempts, I felt frustrated as if I was hanging on the edge of a cliff. Consequently, I went to the section of ordinary differential equations in a library to seek help. After having selected many books from the selves and having disappointedly returned them, suddenly [Was] caught my attention. After I carefully compared the definition given in [Cod, p.148, l.-12-l.-5] with [Was, p.32, Definition], I finally realized that the constant O in [Cod, p.158, (4.41)] can depend on m.

Going to the library is like meeting with experts.
When we feel tired, frustrated, or even hopeless
And try to seek courage, inspiration, or assistance for organization,
We will never be disappointed if we consult with them.
No matter what kind of question we have
Most likely there are some scholars from somewhere
Who have studied the same problem before.
They will climb mountains, sail through seas,
And descend from skies to come to our rescue
Regardless of region, race, or social status.
They break through the barriers of time and space,
Hide on the shelves in the library,
And wait for us to select them.
All of them are selfless.
When one falls,
Another picks up the relay baton, and runs toward us.
They do their best to help us continue their unfinished journey.


1. [Cod] Coddington E. A. & Levinson N.: The Theory of Ordinary Differential Equations, New York: McGraw-Hill, 1955.

2. [Was] Wasow, W.: Asymptotic Expansions for Ordinary Differential Equations , New York: Interscience, 1965.