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Need help to solve one differential equation

  1. Apr 6, 2009 #1
    Does anybody know how to solve this differential equation:

    [tex]
    \frac{d^2 \theta}{dt^2}-A\sin(\theta)-
    \frac{B^2 \cos(\theta)}{ \sin^3(\theta) }=0
    [/tex]

    This is an equation that i get from the brachistochronic motion on the surface of a sphere.
     
  2. jcsd
  3. Apr 6, 2009 #2

    tiny-tim

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    Science Advisor
    Homework Helper

    Welcome to PF!

    Hi TimJ! Welcome to PF! :smile:

    (have a theta: θ and an omega: ω :wink:)
    Try writing d2θ/dt2 = dω/dt = dω/dθ dθ/dt = ω dω/dθ = 1/2 d(ω2)dθ,

    so d(ω2)/dθ = 2Asinθ + 2Bcotθcosec2θ :wink:
     
  4. Apr 7, 2009 #3
    Thank you for your help.
     
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