1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook