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DSolve & Airy Functions


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[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[
              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[1] + 
          AiryBi[(2 b + 2 a x)/(2^(2/3) a^(2/3))]
C[2]}})


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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