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Super-hard differential equation in classical mechanics problem

  1. Sep 17, 2012 #1
    1. The problem statement, all variables and given/known data
    A particle of mass m moves in the following (repulsive) field
    U(x) = α/x², α > 0,
    with α a constant parameter. Determine the (unique) trajectory of the particle, x(t), corresponding to the initial conditions of the form

    x(t0) = x0 > 0,

    x'(t0) = [itex]\sqrt{\frac{2}{m}(E-\frac{α}{(x0)^2})}[/itex]


    2. Relevant equations

    ^

    3. The attempt at a solution

    mx''(t) = -d/dx U(x)
    = - (2α/x³)
    = 2α/x³

    => x''(t) = 2α/mx³

    Would anyone please be able to point me on the right track to solving this stupid DE? It's really starting to mess with my mind now!
     
    Last edited by a moderator: Sep 18, 2012
  2. jcsd
  3. Sep 17, 2012 #2
  4. Sep 17, 2012 #3
    You can solve your "stupid" DE by multiplying both sides of the equation by x'. This will give you exact differentials on both sides.
     
  5. Sep 18, 2012 #4

    vela

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    The DE always speaks well of you.

    This is a good trick to remember.
     
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