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How to integrate this?

  1. Feb 3, 2015 #1
    1. The problem statement, all variables and given/known data
    How to integrate dv/dt=g-kv/m?

    2. Relevant equations
    This is ODE.

    3. The attempt at a solution
    Now what? I don't know how to integrate the left side.
  2. jcsd
  3. Feb 3, 2015 #2


    Staff: Mentor

    The left side can be rewritten as ##\frac{m \ dv}{mg - kv}##. There's a fairly obvious substitution you can use.
  4. Feb 3, 2015 #3
    What substitution?
  5. Feb 3, 2015 #4
    Never mind. I integrated and got (-m/k)ln abs(gm-kv)+C.
  6. Feb 3, 2015 #5
    Now, how to simplify (-m/k)ln abs(gm-kv)=t+C?
  7. Feb 3, 2015 #6

    Stephen Tashi

    User Avatar
    Science Advisor

    Are you saying you can't work [itex] \int {\frac{1}{g- \frac{kv}{m}} }dv [/itex] ?

    Could you do something like [itex] \int (3 -5v)^{-1} dv [/itex] ?
  8. Feb 3, 2015 #7
    No, now I got it. I simplified and got gm-kv=Ce^(-kt/m).
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