Unformatted text preview: vanishes ONLY at x = 0 and the hyperbolic cosine is always positive. If we use the following form of the general solution X = A 3 cosh √ − λx + B 3 then the derivative X wil be X = √ − λA 3 sinh √ − λx + B 3 The Frst boundary condition X (0) = yields B 3 = 0 and clearly to satisfy the second boundary condition we must have A 3 = 0 (recall sinh x = 0 only for x = 0 and the second boundary condition reads √ − λA 3 sinh √ − λL = 0, thus the coeﬃcient A 3 must vanish). Any other form will yields the same trivial solution, may be with more work!!! 16...
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 Fall '08
 BELL,D
 Complex number, hyperbolic cosine, hypebolic sine, shifted hyperbolic cosine, A3 cosh

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