Differential Equations Lecture Work Solutions 327

Differential - Dierentiate(2 with respect to x twice utxx = cuxxx linear terms Linear terms are enough because we have t2 in front Also get uttx =

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Diferentiate (2) with respect to x twice u txx = cu xxx + linear terms Linear terms are enough because we have ∆ t 2 in Front. Also get u ttx = cu xxt + linear terms = c ( cu xxx ) + linear terms = c 2 u xxx + linear terms u ttt = cu xtt + linear terms = c 3 u xxx + linear terms Substitute in (6) u t = cu x + c t 2 4 c 2 u xxx c 2 u xxx + linear terms + +∆ t 2 c 2 4 ( cu xxx + linear terms) + 1 12 c 3 u xxx ! c x 2
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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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