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Second order

  1. Jan 12, 2007 #1
    I was trying to solve a physics problem which led me to an equation of the form:
    d^2x/dt^2 + a/ x = b; Can this be solved without any aproximations beeing made?
     
  2. jcsd
  3. Jan 12, 2007 #2
    Depends.

    Assuming a,b are constants, multiply by [tex]x^{\prime}[/tex], to get

    [tex]x^{\prime} x^{\prime \prime} + a \frac{x^{\prime}}{x} = b x^{\prime}[/tex]

    now integrate to get

    [tex]\frac{x^{\prime}^2}{2} + a \ln{x} = bx + c [/tex]

    (c is a constant). Rearrange to get t as a function of x, i.e.,

    [tex]\frac{1}{\sqrt{2}} \int{\frac{dx}{\sqrt{bx + c - a \ln{x}}}} = t + const.[/tex]

    Other than that, I'm not sure.
     
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