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[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