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simple question on DSolve


Hello,
if I try to solve the simple boundary value problem

y''+ky=0
y'(0)=0
y'(1)=0

mathematica returns me y=0, that is correct but that is not the
complete answer... Does anyone know how to get the complete answer?
(of course i know the complete answer, but I would like to solve some
uglier versions of the same problem...)
Thanks



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