# Another math question...

Jirakon
Posers and Puzzles 06 Oct '08 17:12
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. 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.
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
Baby Gauss
07 Oct '08 15:58
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. Palynka
Upward Spiral
08 Oct '08 08:36
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. ðŸ˜•
Baby Gauss
08 Oct '08 13:59
Originally posted by Palynka
Is that your LaTeX typesetting default? It looks strangely ugly. ðŸ˜•
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.

ðŸ˜³ ðŸ˜³ ðŸ˜³
8. Palynka
Upward Spiral
08 Oct '08 16:19
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.

ðŸ˜³ ðŸ˜³ ðŸ˜³
Enjoy!
http://thornahawk.unitedti.org/equationeditor/equationeditor.php