       DSolve & Airy Functions

• To: mathgroup at smc.vnet.net
• Subject: [mg24545] DSolve & Airy Functions
• From: Gerhard Killesreiter <killesreiter at physik.uni-freiburg.de>
• Date: Mon, 24 Jul 2000 03:04:24 -0400 (EDT)
• Organization: Fakultaet fuer Physik, ALU Freiburg
• Sender: owner-wri-mathgroup at wolfram.com

```Hi!

I ran into the following problem:

DSolve[{-1/2 f''[x] + (a x + b)f[x]  == 0, f[a Infinity] == 0,
f'[a Infinity] == 0}, f[x], x]

gave me:

({{f[x] ->
AiryAi[(2 b + 2 a x)/(2^(2/3) a^(2/3))] C +
AiryBi[(2 b + 2 a x)/(2^(2/3) a^(2/3))] C}, {f[
x] -> AiryAi[(2 b + 2 a x)/(2^(2/3) a^(2/3))] C[
1] + AiryBi[(2 b + 2 a x)/(2^(2/3) a^(2/3))] C[
2]}, {f[x] ->
AiryAi[(2 b + 2 a x)/(2^(2/3) a^(2/3))] C +
AiryBi[(2 b + 2 a x)/(2^(2/3) a^(2/3))]
C}})

That is three times the same solution that I would get without the
boundary conditions. In my opinion the AiryBi part should have been
vanished because of that conditions. Am I wrong?

Cheers,
Gerhard

```

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