Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Science Advisor

    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


    User Avatar
    Staff Emeritus
    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:
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?