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Homework Help: Second Order differential equation involving chain rule

  1. Oct 27, 2013 #1
    1. The problem statement, all variables and given/known data

    Solve d^2x/dt^2 = (3x^3)/2

    when dx/dt = -8 and x = 4 when t = 0

    2. The attempt at a solution

    v = dx/dt dv/dx = d^2/dx^2

    d^2x/dt^2 = v(dv/dx) = (3x^3)/2

    v dv = (3x^3)/2 dx

    integrating and using limits and you get :

    v^2/2 -32 = (3x^4)/8 - 96 ............ 4v^2 = 3x^4 - 512

    this is where I'm stuck I can take the square root of the 4v^2 but not the right hand side because of the three and the 512. I'm not sure if there is another technique I can use but finding the square root of both sides is the only way I was taught to do these problems and its the only example in the book.
    Any help would be appreciated.
  2. jcsd
  3. Oct 28, 2013 #2


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    Homework Helper

    I think you are doing fine up till there. The square root is just sqrt(3x^4-512). But then if you want to find x(t) instead of v(x) you have to integrate something like dx/sqrt(3x^4-512), and that is going into elliptic integral country. I don't think you want to go there. I think you've gotten about as far as you can reasonably expect to get.
  4. Oct 28, 2013 #3
    Alright Thanks I was able to get the question after it anyway I think I'll just leave this one for now.
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