Unformatted text preview: 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 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 cosh x is never zero thus the coeﬃcient A 3 must vanish). Any other form will yields the same trivial solution, may be with more work!!! 21...
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- Fall '08
- Complex number, Hyperbolic function, A3 cosh