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  • Task info Open for submissions from Monday, 25 July 2016, 8:40 PM (2837 days ago)
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Problem 3.38, p. 140, Reference Book

Example 5, p. 100


By setting \fs2 y(x) = e^{S(x)} or \fs2 y(x) = e^{S_a(x)+C(x)} where
\fs2 S(x) \sim S_a(x), find the asymptotic behavior of \fs2 y(x) at large \fs2 x for the following equations:

(a) Modified Bessel equation:  \fs2 x^2 \, y'' + x\, y' - (x^2+\nu^2) \, y=0.

(b) Parabolic cylinder equation:  \fs2 y'' + (\nu + \frac{1}{2} - \frac{1}{4} \, x^2) \, y=0.

(c) Airy equation:  \fs2 y'' =x\, y.