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 2 years ago
consider a boundary value problem y"+ky=0, y(0)=0, Y(pi/2)=0. is it possible to determine the values k for trivial solutions. (b) nontrivial.
 2 years ago
consider a boundary value problem y"+ky=0, y(0)=0, Y(pi/2)=0. is it possible to determine the values k for trivial solutions. (b) nontrivial.

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malevolence19
 2 years ago
Best ResponseYou've already chosen the best response.0\[y''+ky=0 \implies y=A \cos(\sqrt k t)+B \sin(\sqrt k t)\] From here you can plug in the initial conditions

across
 2 years ago
Best ResponseYou've already chosen the best response.0Since the boundary conditions are homogeneous, your nontrivial solution (the case \(k>0\)) will be a Fourier sine series. For \(k\leqslant0\), you'll get trivial solutions.
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