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Math Help - Getting into correct form

  1. #1
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    Getting into correct form

    I'm part way through a question, just need help at the end.

    I found the characteristic equation for a fourth order DE with constant co-efficents (and homogeneous) was r^4 - 2r^2 +1=0 so the roots are r = 1, -1 each with multiplicity 2.

    so y=e^x(A+Bx)+e^{-x}(B+Dx) I need to get it in terms of sinh and cosh. Thanks
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  2. #2
    Super Member ILikeSerena's Avatar
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    Re: Getting into correct form

    You may want to substitute:

    e^x = \cosh x + \sinh x
    e^{-x} = \cosh x - \sinh x
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  3. #3
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    Re: Getting into correct form

    That does the trick. Redefining constants, y=(A+Bx)coshx+(C+Dx)sinhx.
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