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Trascendental equation

  1. Mar 11, 2009 #1
    Hi everybody,

    can anyone help me in finding the analytic solution of the trascendental equation in the attached file?

    A1, alfa1, alfa2, a and b are constants.
    is it possible to solve it by means of Mathematica?


    thanks
    Michele
     

    Attached Files:

  2. jcsd
  3. Mar 11, 2009 #2
    Just write it in tex, I can't view it.
     
  4. Mar 11, 2009 #3
    A1*(tan(xa/alfa2)/tan(xa/alfa1))-tan(xa/alfa2)*tan(xb/alfa2)-A1*(tan(xb/alfa2)/tan(xa/alfa1))=1


    thanks again
     
  5. Mar 11, 2009 #4
    Here's the equation in tex

    [tex]\frac{A_1 \cdot \tan{ax / \alpha_2}}{\tan{ax / \alpha_1}} - \tan{ax / \alpha_2} \cdot \tan{bx / \alpha_2} - \frac{A_1 \cdot \tan{bx / \alpha_2}}{\tan{\ax / \alpha_1}} = 1[/tex]
     
    Last edited: Mar 12, 2009
  6. Mar 12, 2009 #5

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    That appears to be a single equation in two different variables, xa and xb. It will not have a single solution.
     
  7. Mar 12, 2009 #6
    x is the only variable. a and b are real constants. you have to read x*a and x*b and not xa and xb
     
  8. Mar 12, 2009 #7
    So what you really have is

    A*tan(a'x)/tan(b'x) - tan(a'x)*tan(c'x) - A*tan(c'x)/tan(b'x) = 1

    For appropriate choices of a', b', and c'.
     
  9. Mar 12, 2009 #8
    Exactly
     
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