1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
    form.

    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
    someone?
     
  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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Differential equation using complex exponentials
  1. Complex Exponentials (Replies: 6)

Loading...