Differential Equations Lecture Work Solutions 162

Differential Equations Lecture Work Solutions 162 - un = +...

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˙ u n = H cosh H ( L x ) H sinh H L Z x 0 s n ( ξ )s inh H ξdξ + sinh H ( L x ) H sinh H L s n ( x )s inh H x | {z } integrand at upper limit + H cosh H x H sinh H L Z L x s n ( ξ )s inh H ( L ξ ) + sinh H x H sinh H L ± s n ( x )s inh H ( L x ) | {z } integrand at lower limit Let’s add the second and fourth terms up 1 H sinh H L s n ( x ) sinh H ( L x )s inh H x sinh H x sinh H ( L x ) | {z } =0 ¨ u n = H 2 sinh H ( L x ) H sinh H L Z x 0 s n ( ξ )s inh H ξdξ + H cosh H ( L x ) H sinh H L s n ( x )s inh H x + H 2 sinh H x H sinh H L Z L x s n ( ξ )s inh H ( L ξ ) + H cosh H x H sinh H
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This note was uploaded on 12/22/2011 for the course MAP 2302 taught by Professor Bell,d during the Fall '08 term at UNF.

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