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Exponential Solution of Cubic Equation

  1. Jul 9, 2011 #1
    , Dear Fellows
    I need to find the solution of cubic equation in exponential form which is written in a research article

    If EQUATION is

    (k^6-A k^4+B k^2+E)Y(z)=0

    and solution given is as,

    Y(z)=M exp(-k_1z)

    where M is a constant and k_1 is solution of the above equation.

    Any Reply Will Be Informative,
  2. jcsd
  3. Jul 9, 2011 #2


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    I can't make heads or tails out of what you have written. The equation you write:
    (k^6-A k^4+B k^2+E)Y(z)=0 simply tells us that, for some z, Y(z)= 0. It does NOT say that this is a cubic equation and Y could be anything.
  4. Jul 9, 2011 #3


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    Gold Member

    It looks like you were solving a 6th order differential equation in Y?
    [tex][D_z^6 - A D_z^4 + D_z k^2 + E]Y(z)=0[/tex]
    There is a cubic formula but it's pretty messy, especially if you are leaving A,B, and E arbitrary. Google "cubic formula" and you'll find many links. The wikipedia article is a good reference: http://en.wikipedia.org/wiki/Cubic_function" [Broken]
    Last edited by a moderator: May 5, 2017
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