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Solve this ODE

  1. Jan 17, 2004 #1
    I’ve been trying to find an analytic solution to the following ODE. I haven’t been successful and have come to the conclusion that an analytic solution probably doesn’t exist. I am not totally sure though and would be appreciative if you guys gave it a look.

    a & b are arbitrary constants...

    \ddot{f} + b tan(b t) \dot{f} - a^2 cos^2(b t) f = 0

    Thanks in advance...
    Last edited by a moderator: Jan 17, 2004
  2. jcsd
  3. Jan 17, 2004 #2
    First, write the tan as sin/cos. Then multiply the equation by cos(bt). Then write the equation in terms of the variable:

    [tex] \tau = \sin bt [/tex]

    Last edited: Jan 17, 2004
  4. Jan 18, 2004 #3
    Thanks for the hint. I actually found this substitution works best…

    [tex] \tau = cos(bt) [/tex]

    after making the substitution I solved it via a power series method.
  5. Jan 19, 2004 #4
    But you can solve it exactly if you use the other one!!!
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