Unformatted text preview: 3 cosh √ − λx + B 3 Or X = A 4 sinh √ − λx + B 4 Which form to use, depends on the boundary conditions. Recall that the hypebolic sine vanishes ONLY at x = 0 and the hyperbolic cosine is always positive. If we use the following form of the general solution X = A 4 sinh √ − λx + B 4 then the derivative X wil be X = √ − λA 4 cosh √ − λx + B 4 The Frst boundary condition X (0) = 0 yields B 4 = 0 and clearly to satisfy the second boundary condition √ − λA 4 cosh √ − λL = 0 we must have A 4 = 0 (recall cosh x is never zero thus the coeﬃcient A 4 must vanish). 23...
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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.
 Fall '08
 BELL,D

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