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A Weird Differential equation

  1. Sep 9, 2008 #1
    Hi Folks..I came up with a weird looking DE for my research

    Q''[t] = f[t]Q'[t] + g[t]Q[t] + h[t]*Sqrt[(Q[t])^2 + (k[t]Q'[t])^2]

    The thing that mixes my mind is the square root term..If there is no square root terms it would like a riccati type..but there is..i tried to google it but it just showed me bunch of papers about fractional power DEs which is different...Is there any classification for this type ?

  2. jcsd
  3. Sep 11, 2008 #2
    Common any ideas ?
  4. Sep 18, 2008 #3
    Actually, setting:

    [tex]Q(t)=e^{\int_0^t dx G(x)}[/tex]

    reduces your 2nd order ODE to a 1st order nonlinear one:

    [tex]G'(t)=-G(t)^2+f(t) G(t)+g(t)+h(t) \sqrt{G(t)^2 k(t)^2+1}[/tex]

    Depending on the form of the functions f(t),h(t), g(t) and k(t) you might be able to solve the latter and then again it might be worse...
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