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Integral Transform problem

  1. Apr 15, 2007 #1
    1. The problem statement, all variables and given/known data

    L[cos(at)cosh(at)] = ?

    2. Relevant equations

    L[cos(at)] = s/(s^2 + w^2)

    3. The attempt at a solution

    I'm able to get the solution given that is (s^3)/(s^4 + 4a^4)

    The question requested to use first shift property. So I used cosh(at) = 1/2[e^at + e^(-at)]

    but now I'm trying to use another method.

    if you use euler's rule, you can also get cos(at) = cosh(at) = 1/2[e^at + e^(-at)]

    then simply multiply them and get L[e^2at + 2 + e^(-2at)] but I dont seem to get the same solution as above, any ideas? :frown:
  2. jcsd
  3. Apr 15, 2007 #2


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    Staff Emeritus
    Science Advisor

    No, Euler's rule does NOT say cos(at)= cosh(at)!
    You may be thinking of
    [tex]cos(at)= \frac{e^{iat}+ e^{-iat}}{2}[/tex]
    Note the "i" s in that!

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