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Posers and Puzzles

Posers and Puzzles

  1. 06 Oct '08 17:12
    It's been a while since I've done differential equations...

    v'(t) - k [v(t)]^2 = g

    Solve for v(t).

    I'd know what to do if the v weren't squared, but I have no idea what to do here.
  2. Standard member PBE6
    Bananarama
    07 Oct '08 01:00
    Originally posted by Jirakon
    It's been a while since I've done differential equations...

    v'(t) - k [v(t)]^2 = g

    Solve for v(t).

    I'd know what to do if the v weren't squared, but I have no idea what to do here.
    Had to look at this one for a while, but I finally got something simple:

    v'(t) = k[v(t)]^2 + g = (SQRT(k)*v + i*SQRT(g)) * (SQRT(k)*v - i*SQRT(g))

    Putting this into a more useable form, we have:

    dv / ((SQRT(k)*v + i*SQRT(g)) * (SQRT(k)*v - i*SQRT(g))) = dt

    Now just separate the fractions and integrate each one. I have to split, but the answer should follow simply from here. (If no one finishes it, I'll do it when I get home.)
  3. 07 Oct '08 05:07
    That's fine. I just used partial fractions from there. Thanks.
  4. Standard member adam warlock
    Baby Gauss
    07 Oct '08 10:34
    Originally posted by Jirakon
    It's been a while since I've done differential equations...

    v'(t) - k [v(t)]^2 = g

    Solve for v(t).

    I'd know what to do if the v weren't squared, but I have no idea what to do here.
    I dropped the v dependence in t in intermediary calculations for the sake of a lighter notation.

    http://i35.tinypic.com/5bv0h5.gif
  5. Standard member adam warlock
    Baby Gauss
    07 Oct '08 15:58
    Originally posted by adam warlock
    I dropped the v dependence in t in intermediary calculations for the sake of a lighter notation.

    http://i35.tinypic.com/5bv0h5.gif
    I forgot to add the constant of integration so the last two steps should be -1/v=kt+C which implies v(t)=-1/(kt+C) where C depends on the initial conditions
  6. Standard member Palynka
    Upward Spiral
    08 Oct '08 08:36
    Originally posted by adam warlock
    I dropped the v dependence in t in intermediary calculations for the sake of a lighter notation.

    http://i35.tinypic.com/5bv0h5.gif
    Is that your LaTeX typesetting default? It looks strangely ugly.
  7. Standard member adam warlock
    Baby Gauss
    08 Oct '08 13:59
    Originally posted by Palynka
    Is that your LaTeX typesetting default? It looks strangely ugly.
    Shamed as I am of admitting it, but it isn't LateX. It was done using MathType and then I exported the solution into a .gif image.

    I wasn't at my machine and so couldn't use LateX.

  8. Standard member Palynka
    Upward Spiral
    08 Oct '08 16:19
    Originally posted by adam warlock
    Shamed as I am of admitting it, but it isn't LateX. It was done using MathType and then I exported the solution into a .gif image.

    I wasn't at my machine and so couldn't use LateX.

    Enjoy!
    http://thornahawk.unitedti.org/equationeditor/equationeditor.php
  9. Standard member adam warlock
    Baby Gauss
    08 Oct '08 19:09 / 1 edit
    Originally posted by Palynka
    Enjoy!
    http://thornahawk.unitedti.org/equationeditor/equationeditor.php
    Nice!

    http://tinyurl.com/4n4uhn