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Can this equation be solved?

  1. May 25, 2010 #1
    Hi,

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

    [tex](2t+1)e^{-2t}=5[/tex]

    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.

    Cheers
     
  2. jcsd
  3. May 25, 2010 #2

    Cyosis

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    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:

    [itex]f(t)e^{f(t)}=k[/itex]

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

    [itex]f(t)=W(k)[/itex]

    how about then I just multiply by -1:

    [itex]-(2t+1)e^{-2t}=-5[/itex]

    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 :)
     
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