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Need help solving second order DE.

  1. Jan 2, 2010 #1
    Hello, I hope I am writing to right part of a forum...

    I made a differential equation when I was solving my problem, but unfortunately I am not capable of solving such equation since I am only 12th grader.
    Or maybe it is not possible to solve it at all??

    [tex] \frac{5\sqrt{3}}{18}\frac{d^{2}x}{dt^{2}} = 5 - \frac{3\sqrt{3}}{R}\frac{dx}{dt}[/tex]

    R is unknown.

    [tex]\frac{d^{2}x}{dt^{2}} = x(t) [/tex]

    [tex]\frac{dx}{dt} = v(t)[/tex]

    v(0) = 0
    v(5) = 15

    I need to find equation describing x(t). Jap, v is velocity, and nope it is not my homework.

    It would be great if someone help me a bit, in school do not teach how to solve differential equations, nor second order. :)
  2. jcsd
  3. Jan 2, 2010 #2


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    Homework Helper

    If R is constant, then you have a 2nd order DE with constant coefficients. Which can be solved by writing down the roots of the auxiliary equation.
    http://www.efunda.com/math/ode/linearode_consthomo.cfm" [Broken]
    Last edited by a moderator: May 4, 2017
  4. Jan 3, 2010 #3
    Yes R is a constant.
    Okay I guess I understood a bit:

    [tex]x(t) = c_{1}e^{\frac{18(\sqrt{\frac{27}{R^{2}}+\frac{50\sqrt{3}}{9}}-\frac{3\sqrt{3}}{R})}{5\sqrt{3}}t}+c_{2}e^{-\frac{18(\sqrt{\frac{27}{R^{2}}+\frac{50\sqrt{3}}{9}}+\frac{3\sqrt{3}}{R})}{5\sqrt{3}}t}[/tex]

    anyway to me it gets too crazy.


    is it possible to solve this equation normally that I would know R & c1 & c2 ?
    Last edited: Jan 3, 2010
  5. Jan 3, 2010 #4


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    Since you have three unknowns you'd need at least one more condition to find R.
  6. Jan 3, 2010 #5
    I understood, thanks for help!
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