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Examining the graphs of the solutions of the Airy equation for

It is easy to
see that there is no oscillatory behavior, but are there any solutions
that are bounded? An interesting computer exercise for the student is
to try varying the initial values for the velocity ,
while holding fixed, in order to find an experimental value for
that gives a bounded solution. (We selected to make
the experiment more interesting, since gives the trivial
solution.) Our computer experiments indicate that if , the solution appears to remain bounded as **t** becomes large
negative.
To find out what is really going on, we turn to the Riccati equation
associated with the Airy equation .

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