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Chem Differential Eq HW Solutions Fall 2011 98

Chem Differential Eq HW Solutions Fall 2011 98 - k a µ...

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98 Chapter 6 Sturm-Liouville Theory with Engineering Applications But y satisfies the boundary condition y ( a ) = - κy ( a ), so 2 λ 2 a 0 [ y ( r )] 2 rdr = a 2 κ 2 [ y ( a )] 2 + λ 2 a 2 [ y ( a )] 2 ; a 0 [ y ( r )] 2 rdr = a 2 2 κ 2 [ J 0 ( λ k a )] 2 λ 2 k + [ J 0 ( λ k a )] 2 = a 2 2 [ J 0 ( λ k a )] 2 + [ J 1 ( λ k a )] 2 , because, by (7), [ J 0 ( λ k a )] 2 = λ k κ J 1 ( λ
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Unformatted text preview: λ k a ) µ 2 . (b) Reproduce the sketch oF prooF oF Theorem 1. The given Formula For the coeffi-cients is precisely Formula (5) in this case....
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