Differential Equations Lecture Work Solutions 167

Differential Equations Lecture Work Solutions 167 - 5.4.3...

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5.4.3 One Dimensional Boundary Value Problems Problems 1. Find the eigenvalues and corresponding eigenfunctions in each of the following boundary value problems. (a) y 0 λ 2 y =0 0 <x<a y 0 (0) = y 0 ( a )=0 (b) y 0 λ 2 y 0 y (0) = 0 y ( a )=1 (c) y 0 + λ 2 y 0 y (0) = y 0 ( a (d) y 0 + λ 2 y 0 y (0) = 1 y 0 ( a 2. Find the eigenfunctions of the following boundary value problem. y 0 + λ 2 y 0 <x< 2 πy (0) = y (2 π ) y 0 (0) = y 0 (2 π ) 3. Obtain the eigenvalues and eigenfunctions of the problem. y 0 + y 0 +(
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