- 07 Oct '08 01:00

Had to look at this one for a while, but I finally got something simple:*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.

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.) - 07 Oct '08 10:34

I dropped the v dependence in t in intermediary calculations for the sake of a lighter notation.*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.

http://i35.tinypic.com/5bv0h5.gif - 07 Oct '08 15:58

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*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 - 08 Oct '08 16:19

Enjoy!*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.

http://thornahawk.unitedti.org/equationeditor/equationeditor.php