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Math Help - ODE and Linear Algebra

  1. #1
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    ODE and Linear Algebra

    y'' = +λ^2*y
    Show cosh( λt) and sinh( λt) form an alternate basis for our
    λ^2– eigenspace.

    Any help fellas?
    Last edited by thehollow89; April 5th 2009 at 12:01 PM.
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  2. #2
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    Quote Originally Posted by thehollow89 View Post
    y'' = +λ^2*y
    Show cosh( λt) and sinh( λt) form an alternate basis for our
    λ^2 eigenspace.

    Any help fellas?
    You just need to show that \sinh (\lambda x) and \cosh (\lambda x) are linearly independent (here it is assumed that \lambda > 0) solutions to the differencial equation. To see that just use the Wronskian.
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