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: Can this equation be solved?

  1. May 25, 2010 #1

    I'm wondering if there is an exact solution to:


    I've tried and have been unable to solve this for t. I can get an approximate numerical answer using the calculator but that's it.

  2. jcsd
  3. May 25, 2010 #2


    User Avatar
    Homework Helper

    There is no exact solution in terms of elementary functions. You can however find a close formed solution by using the Lambert W-function.
  4. May 25, 2010 #3
    How about if I start it for you and see if you can finish it. You want to get it into a form:


    so that you can then take the Lambert-W of both sides and write:


    how about then I just multiply by -1:


    see how I'm starting to build the exponent to look like it's coefficient. What else then would I have to do to get it into Lambert-W form?
  5. May 25, 2010 #4
    Thanks for the help guys, I've got it now :)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook