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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.
 one year ago
 one year 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.
 one year ago
 one year ago

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malevolence19Best 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
 one year ago

acrossBest ResponseYou've already chosen the best response.0
Since 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.
 one year ago
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