As part of a separable solution to a PDE, I get the following ODE:(adsbygoogle = window.adsbygoogle || []).push({});

X''-rX=0 (*),

with -infty<x<infty and the boundary condition X(+/-infty)=0 (X is an odd function here). Thus I have assumed r>0 to avoid the periodic solution, cos. I, therefore, argue that the solution is the symmetric ~exp(-sqrt(r)|x|). This, however, has a discontinuity at x=0 which, seems to me, contrasts with (*) which implies X' and X'' must be continuous across x=0.

Any ideas? (Many thanks.)

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# Solution to ODE

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