Differential Equations Lecture Work Solutions 162

# Differential Equations Lecture Work Solutions 162 - un = n...

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˙ u n = n π H cosh n π H ( L x ) n π H sinh n π H L x 0 s n ( ξ ) sinh n π H ξ dξ + sinh n π H ( L x ) n π H sinh n π H L s n ( x ) sinh n π H x integrand at upper limit + n π H cosh n π H x n π H sinh n π H L L x s n ( ξ ) sinh n π H ( L ξ ) + sinh n π H x n π H sinh n π H L s n ( x ) sinh n π H ( L x ) integrand at lower limit Let’s add the second and fourth terms up 1 n π H sinh n π H L s n ( x ) sinh n π H ( L x ) sinh n π H x sinh n π H x sinh n π H ( L x ) = 0 ¨ u n = n π H 2 sinh n π H ( L x ) n π H sinh n π H L x 0 s n ( ξ ) sinh n π H ξ dξ + n π H cosh n π H ( L x ) n π H sinh n π H L s n ( x ) sinh n π H x + n π H 2 sinh n π H x n π H sinh n π H L L x s n ( ξ ) sinh n π H ( L ξ ) + n π H cosh n π H x n π H sinh n π H L s n ( x ) sinh
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