Problem5.3.3 - ‡ Problem 5.3.3 Multiplying the ODE...

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Unformatted text preview: ‡ Problem 5.3.3 Multiplying the ODE through by H HxL we get But, „2 f „f H HxL ÅÅÅÅÅÅÅÅÅÅ + H HxL a HxL ÅÅÅÅÅÅÅ + h HxL 8l b HxL + g HxL< f = 0 „ x2 „x „2 f „ „f „H „f H HxL ÅÅÅÅÅÅÅÅÅÅ = ÅÅÅÅÅÅÅ JH ÅÅÅÅÅÅÅ N - ÅÅÅÅÅÅÅ ÅÅÅÅÅÅÅ „ x2 „x „x „x „x Substituting into the previous expression and collecting terms gives „ „f „f „H ÅÅÅÅÅÅÅ JH ÅÅÅÅÅÅÅ N + ÅÅÅÅÅÅÅ JH a - ÅÅÅÅÅÅÅ N + Hl b + gL H f = 0 „x „x „x „x Hence to be in standard Sturm-Liouville form, we must have „h ÅÅÅÅÅÅÅ = a H, or H HxL = C1 Exp A‡ a HtL „ tE „x (1) (2) (3) x If we let C1 = 1, then p HxL = H, q HxL = g H, and s HxL = b H (4) (5) ...
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This note was uploaded on 02/18/2010 for the course ENGINEEING 32145 taught by Professor Stroeve during the Fall '09 term at Universidad de Carabobo.

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