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.)