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Is this separable

  1. Jul 1, 2010 #1
    How do you find a solution for:

    2tv' - v = 0

    The text says it's separable but I'm not seeing it. I'm just learning so extra details are appreciated. Thanks.

    (this should have been posted in the homework section - but I can't seem to move it there, sorry)
    Last edited: Jul 1, 2010
  2. jcsd
  3. Jul 1, 2010 #2


    Staff: Mentor

    2t dv/dt = v
    ==> 2t dv = v dt
    Can you continue?
  4. Jul 1, 2010 #3
    well I think I want to switch things around so v and t are separated

    1/v dv = 1/2t dt

    integrating both sides
    ln(v) = 1/2 ln(t)+C

    e^x both sides:
    v = k*sqrt(t)

    Which looks right! Is that how I was meant to do it? If so, thanks - I got stalled before when I got the ln() on both sides.
  5. Jul 1, 2010 #4


    Staff: Mentor

    Looking right might not be good enough. You can check by taking the derivative and verifying that tv' - v = 0.
  6. Jul 3, 2010 #5
    Verifying that 2tv' - v = 0 :smile:
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