Question

(a) Consider the Sturm-Liouville problem y'' + ky = 0, y(0) = 0, y'(2) = 0. Let the eigenvalues be denoted $k_1, k_2, \dots$, where $|k_1| < |k_2| < \dots$ $k_n = (2n+1)^2(\frac{\pi^2}{8})$ (b) Now consider the Sturm-Liouville problem y'' + ky = 0, y(0) = 0, y(2) = 0. Let the eigenvalues be denoted $k_1, k_2, \dots$, where $|k_1| < |k_2| < \dots$ $k_3 = $ (c) Consider the Sturm-Liouville problem y'' + ky = 0, 2y(0) + 2y'(0) = 0, \gamma y(2) - 2y'(2) = 0. Find the value of $\gamma$ for which $k = 0$ is an eigenvalue. $\gamma = $

          (a) Consider the Sturm-Liouville problem
y'' + ky = 0, y(0) = 0, y'(2) = 0.
Let the eigenvalues be denoted $k_1, k_2, \dots$, where $|k_1| < |k_2| < \dots$
$k_n = (2n+1)^2(\frac{\pi^2}{8})$
(b) Now consider the Sturm-Liouville problem
y'' + ky = 0, y(0) = 0, y(2) = 0.
Let the eigenvalues be denoted $k_1, k_2, \dots$, where $|k_1| < |k_2| < \dots$
$k_3 = $
(c) Consider the Sturm-Liouville problem
y'' + ky = 0, 2y(0) + 2y'(0) = 0, \gamma y(2) - 2y'(2) = 0.
Find the value of $\gamma$ for which $k = 0$ is an eigenvalue.
$\gamma = $

(a) Consider the Sturm-Liouville problem
y” + ky = 0, y(0) = 0, y'(2) = 0.
Let the eigenvalues be denoted k1, k2, …, where |k1| < |k2| < …
kn = (2n+1)^2((π^2)/(8))
(b) Now consider the Sturm-Liouville problem
y” + ky = 0, y(0) = 0, y(2) = 0.
Let the eigenvalues be denoted k1, k2, …, where |k1| < |k2| < …
k3 =
(c) Consider the Sturm-Liouville problem
y” + ky = 0, 2y(0) + 2y'(0) = 0, γy(2) - 2y'(2) = 0.
Find the value of γ for which k = 0 is an eigenvalue.
γ =

Added by Isabel J.

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