1. Not finding help here? Sign up for a free 30min 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!

How to solve this non lenear equation

  1. May 11, 2009 #1
    [tex]
    v_0=100e^{\frac{-v_0}{100}}\\
    \ln {v_0}=\ln{e^{\frac{-v_0}{100}}}^{100}\\
    [/tex]
    the answer is [tex]v_0=56.7[/tex]
    how to find [tex]v_0[/tex]
    ??
     
  2. jcsd
  3. May 11, 2009 #2

    Mark44

    Staff: Mentor

    You can't solve this type of equation by algebraic means, but you can use approximation techniques to get an approximate solution, which v0 = 56.7 appears to be.
     
  4. May 11, 2009 #3

    Shooting Star

    User Avatar
    Homework Helper

    This is one way of doing it.

    [tex]
    v_0=100e^{\frac{-v_0}{100}}.
    [/tex]


    Putting [itex]
    {\textstyle{{{\rm v}_{\rm 0} } \over {100}}} = x, x = e^{ - x} \Rightarrow x = 1 - x + x^2 /2,
    [/itex] retaining up to the second order term after expanding [itex]e^{-x}.[/itex]

    Now solve for x to get the approximate value. Justify why you are neglecting one value.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: How to solve this non lenear equation
Loading...