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For the boundary value problem,
$y''+\lambda y=0$
$y(-π)=y(π)$ , $y’(-π)=y’(π)$
to each eigenvalue $\lambda$, there corresponds

  1. Only one eigenfunction
  2. Two eigenfunctions
  3. Two linearly independent eigenfunctions
  4. Two orthogonal eigenfunctions

I have tried to solve the problem but could not get my calculations right. Can somebody help?

  • 1
    Surely you know the general solution of the equation $y''+\lambda y=0$. Once this is written down, you might want to examine points 1. to 4.2012-12-19

2 Answers 2