Let L be a nonzero real number (a) Show that the boundary value problem y ' ' y 0, y(0) 0, y(L) 0 has only the trivial solution y 0 for the cases 0 and 0 (b) For the case 0, find the values of for which this problem has a nontrivial solution and give the corresponding solution ...

a Case 1 X 0 y y 0 0 which has an auxiliary equation r 0 where y0 0 ...

Let L be a nonzero real number. (a) Show that the boundary-value problem y'' + y =

Question:

Let L be a nonzero real number.
(a) Show that the boundary-value problem y'' + λy = 0, y(0) = 0, y(L) = 0 has only the trivial solution y = 0 for the cases λ = 0 and λ < 0.
(b) For the case λ > 0, find the values of λ for which this problem has a nontrivial solution and give the corresponding solution.

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