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Unable to solve a nonlinear DE analytically help needed

  1. Apr 15, 2012 #1
    Hi all,

    I have a nonlinear differential equation and I need to find an analytic solution for it. Here it is:

    [tex]\ddot{S}=-{1 \over 6} \dot{S}-{2 \over 7}(1-S)^2(- \dot{S})^{1.3}[/tex]

    I have used a transformation to simplify it:

    [tex]-\dot S = v[/tex]

    and came up with this DE which I couldn't solve it:

    [tex]{{dv} \over {dS}} ={1 \over 6} - {2 \over 7} (1-S)^2 v ^ {0.3}[/tex]

    Anyone who can solve them?

    Bests,

    Ali
     
  2. jcsd
  3. Apr 16, 2012 #2
    shouldnt you have

    [tex]{{dv} \over {dS}} ={1 \over 6}v - {2 \over 7} (1-S)^2 v ^ {0.3}[/tex]
     
  4. Apr 16, 2012 #3
    Unfortunately not. It's not a Bernoulli? DE.
     
  5. Apr 16, 2012 #4
    [tex]S(t)=k[/tex]
     
  6. Apr 16, 2012 #5
    a bit more sophisticated solution, please!
     
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