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Homework Help: Differential equation using complex exponentials

  1. Sep 22, 2011 #1
    1. The problem statement, all variables and given/known data
    Find three independent solutions to the differential equation
    [itex]\frac{d^3}{dt^3}[/itex]f(t) + f(t) = 0
    You should use complex exponentials to derive the solutions, but express the results in real

    2. Relevant equations

    [itex]sin\theta = \frac{e^{i\theta} - e^{-i\theta}}{2i}[/itex]
    [itex]cos\theta = \frac{e^{i\theta} + e^{-i\theta}}{2}[/itex]

    3. The attempt at a solution
    I'm not entirely sure what to do.. please help
    I copy notes in class, tried to read the chapter but I don't see anything that helps me get the question
  2. jcsd
  3. Sep 22, 2011 #2
  4. Sep 22, 2011 #3
    I would recommend trying a solution of the form f(t) = A sin (theta) + B cos (theta) where you can replace the sin and cos with the relevant equations.

    Once you establish the function then differentiate and solve for your A and B.
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