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Need to solve the following differential equation

  1. Apr 28, 2004 #1
    Sorry if this is in the wrong section, I wasn't sure where to post it.

    Can anyone help me - I need to solve the following differential equation and find the values of c and B.

    > k is given as -98.3146.
    > v = 55 when t = 9
    > v = 50 when t = 10

    k(v^2) + B = m.(dv/dt)

    Am I right in thinking that by separation of variables and integration I get

    arctan(v/sqrt(B/k))=kt/m + c


    But then if so, how do I find the values of c and B?

    Thanks for any help,

  2. jcsd
  3. Apr 28, 2004 #2


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    Your solution would be OK, except that k is negative. Note that you are taking the square root of k. The proper way to do this gets you an inverse hyperbolic tangent, not an arctan.

    Also, your k on the rhs should be sqrt(Bk)
    Last edited: Apr 28, 2004
  4. Jul 5, 2004 #3
    First, I don't see any C in the equation to solve, so I assume it's the constant of integration.
    I got:
    [tex]\frac{\sqrt{B}}{\sqrt{k}}\tanh{\frac{\sqrt{B}\sqrt{k}\cdot t+C \sqrt{B}\sqrt{k}\cdot m}{m}}[/tex]
    Last edited: Jul 5, 2004
  5. Jul 5, 2004 #4
    You could also try the "homogeneous + particular" approach.
  6. Jul 5, 2004 #5


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    Science Advisor

    No, you can't because this is a non-linear equation. The whole point of linear equations is that you can solve separate parts of the problem, then put them together. With non-linear equations you can't do that.
  7. Jul 5, 2004 #6
    Yes, you're right. :blush:
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