1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Need help with integration

  1. Oct 17, 2009 #1
    1. The problem statement, all variables and given/known data
    Using the following equations,
    dX/dt = uX

    Derive the following equation:
    u0*t = (KS*YX/S + S0*YX/S + X0) * ln(X/X0) - (KS*YX/S)/(S0*YX/S + X0) * ln{(S0*YX/S + X0 - X)/(S0*YX/S)}

    2. Relevant equations
    u =u0*S/(KS + S)
    YX/S = (X - X0)/(S0 -S)

    3. The attempt at a solution
    Using the equation for YX/S, I solved for S and then plugged that and the equation for u into the equation for dx/dt. After some rearranging and use of common denominators, I have the following:

    u0*dt = (YX/S*KS + YX/S*S0 - X + X0)/{X*(YX/S - X + X0)} dx

    Integration of the left side is easy and results in u0*t but I'm still struggling with the left side.

    Can anybody please help? My calculus is a little rusty. I have to be able to show my work so using a integration calculator won't work. Thanks!
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Oct 18, 2009 #2
    I see that numerous people have viewed my post but nobody has replied. Does this mean that the problem is as difficult as I think it is? :-(
  4. Oct 18, 2009 #3


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    I'm guessing the problem is stated so poorly nobody can figure out what the problem actually is. You give a simple DE with X in terms of t and the answer contains all kinds of other variables -- K, Y, S and "relevant equations" that don't seem to have anything to do with the original.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook