[Algorithms] Looking for a differential equation closed form

[Jon W. <jw...@gm...>]

I'm looking for a closed form solution for a differential equation. I did
pass this stuff 20 years ago, but was more interested in graph theory,
discrete math and DSP, so it's all vanished from my brain :-)

The equation is given a point mass that leaves a start position with a start
velocity. On this point mass is acting a fixed gravitational force (in a
fixed direction), as well as a linear and quadratic motion-opposed force
(air drag) based on a linear and quadratic coefficient of air drag. So far,
it's pretty much your standard "cannonball" equation (although I'd really
appreciate a convenient reference for this solution, too). However, in this
case, I also want to make the drag coefficients a linear function of time --
drag(linear, quadratic) = const(linear, quadratic) + factor(linear,
quadratic) * time.

If someone could plug this into Mathematica (or look it up in a handy
formula reference), I'd really appreciate it. If someone could take the time
to point at the proper online reference, that'd be wonderful, too!

Sincerely,

jw


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