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Thread: PDE problem

  1. #1
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    PDE problem

    I'm following an example for the separation of varibales method from a book and they went from
    $\displaystyle Y_1 '' -pi^2 Y_1 = 0$
    $\displaystyle Y_2 '' -4pi^2 Y_2 = 0$

    to
    $\displaystyle Y_1 (y) = Acosh(pi*y) + B_1 sinh(2pi*y)$
    $\displaystyle Y_2 (y) = A_2 cosh(2pi*y) + B_2 sinh(2pi*y)$

    Can someone explain how they made that jump?

    Thanks
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  2. #2
    Super Member wingless's Avatar
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    Istanbul
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    General solution to the differential equation $\displaystyle y''= k \cdot y$ is,

    $\displaystyle y = A \cosh (\sqrt{k} x) + B \sinh (\sqrt{k} x)$
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  3. #3
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    Thanks!
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