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Solving equation

  1. Mar 12, 2008 #1
    hi there;
    plz can any one help me solving this
    3((e^x)-1)-xe^x=0
    sorry i couldn't use more elegant form to write the equation
    i use some software and they help
    but i cant do it in hand
     
  2. jcsd
  3. Mar 12, 2008 #2
    [tex]3(e^{x}-1)-xe^{x}=0 [/tex] I do not believe you can solve this one algebraically, one can only approximate the solution to these kind of equations.
     
  4. Mar 12, 2008 #3
    i think a graphical method is usefull...

    ciao
     

    Attached Files:

  5. Mar 13, 2008 #4
    thanx for the reply up there
    but i search more and i found this kind of equation can be solved using
    Lambart w-function
    or omega function, the problem i couldnt have more information about this function else some expansion series and i cant even write a code to solve or to find a value in lambart function
    any more help will be useful
    thanx
     
  6. Mar 13, 2008 #5
    can you help me using the latex
     
  7. Mar 13, 2008 #6
    By inspection we can see x=0 is a solution. Do you have any reasoning to believe there are other solutions?

    Edit = maybe I was to hasty - there seems that there is at least one more solution.
     
    Last edited: Mar 13, 2008
  8. Mar 13, 2008 #7

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    If you click on the formula, you will see the code in a new window.
     
  9. Mar 14, 2008 #8
    tanx for the reply
    the 0 solution i know about it
    and there is another solution if you graph the equation you can find it approximately
    its about 2.something
     
  10. Mar 14, 2008 #9
    by the way
    this equation is a result for the Blanck's low and Wien's displacment low
    i want to calculate the Wien's constant at the maximum wave length of black body radiation
    so
    i differentiate Blanck's low and solve the equation for which x have a maximum value
    and the result is something like this equation
    which now i need to solve for x to find max and min value
     
  11. Mar 14, 2008 #10
    Hello Hamamo, if you want some code to calculate the Lambert W function, you might consider using the definition of it and the method of Newton-Raphson. The definition as you might know is:

    [tex]X=Ye^Y \qquad \rightarrow \qquad Y=W(X)[/tex]

    Thus if you define a function f as:

    [tex]f=Ye^Y-X[/tex]

    You can use the method of Newton Raphson to be for calculating this function:

    [tex]Y_{n+1}=Y_n-\frac{Y_ne^{Y_n}-X}{e^{Y_n}(Y_n+1)}[/tex]

    Or:

    [tex]Y_{n+1}=\frac{e^{Y_n}Y_n^2+X}{e^{Y_n}(Y_n+1)}[/tex]

    Take 0 as start value and use this iterative scheme to calculate the solution as the resulting value of the Lambert W function. It converges extremely fast. 5 iterations for the value of the function you are looking to solve.

    best regards, Coomast

    [Edit] The results of the iteration if you use it on your function:
    step n Yn Yn+1
    1 0 -0.149361
    2 -0.149361 -0.177647
    3 -0.177647 -0.178560
    4 -0.178560 -0.178561
    5 -0.178561 -0.178561

    Which is x-3, thus x=2.821439 is the one you need
     
    Last edited: Mar 14, 2008
  12. Mar 14, 2008 #11
    thanx coomast
    you r helpfull thats what i need
    thanx again
     
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