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What exactly is a 2nd order differential equation?

  1. Oct 5, 2012 #1
    A first order DE models the rate of change, e.g. when decay is proportional to time we have the DE: dM/dt = -K.M; this is describing that rate of change mathematically. Am I correct in saying that a 2nd order DE describes the rate of rate of change?

    Also, can anyone explain any application of 2nd order DEs to me? I understand it mathematically, but I am interested in how it works in practice like that decay example I pointed out above, hence this post.
  2. jcsd
  3. Oct 5, 2012 #2

    D H

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    Classical physics is chock full of second order ODEs. F=ma, for example.
  4. Oct 5, 2012 #3


    Staff: Mentor

    Not to mention electrical circuits with an inductor, resistor, and capacitor.
  5. Oct 5, 2012 #4
    Thanks, but can you go through an example with me? actually point out a real life application (which you guys did) but also deriving a 2nd order DE to model it step by step.
  6. Oct 5, 2012 #5


    Staff: Mentor

  7. Oct 10, 2012 #6


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    If you throw a ball directly upward with initial speed 10 m/s, the basic physic law is "force= mass times acceleration". In this case, the only force (neglecting air resistance) is gravity: -mg. Since acceleration is the second derivative of the position function, taking x to be the height above the ground at time t, we have the differential equation
    [tex]m\frac{d^2x}{dt^2}= -mg[/tex]
    with initial conditions x(0)= 0, x'(0)= 10.
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