I am being asked to find ##\lambda## such that ##y'' + \lambda y = 0; ~y(0) =0; ~y'( \pi ) = 0##. This is an eigenvalue problem where we are given boundary conditions. ##\lambda## can be found such that we don't have a trivial solution if we test the different cases when ##\lambda < 0, \lambda = 0##, or ##\lambda > 0##, and solve for what ##\lambda## must be such that we have non-trivial solutions.(adsbygoogle = window.adsbygoogle || []).push({});

I'm just curious as to why these problems are given with boundary conditions instead of initial conditions. Is there some theory behind why we need boundary conditions in order to determine the eigenvalues? Would being given initial conditions allow us to do the same thing?

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# I BVP vs IVP when solving for eigenvalues

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