Solve Trascendental Equation Analytically with Mathematica

[mike79]

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

 

[Santa1]

Just write it in tex, I can't view it.

 

[mike79]

A1*(tan(xa/alfa2)/tan(xa/alfa1))-tan(xa/alfa2)*tan(xb/alfa2)-A1*(tan(xb/alfa2)/tan(xa/alfa1))=1


thanks again

 

[qntty]

Here's the equation in tex

$$\frac{A_1 \cdot \tan{ax / \alpha_2}}{\tan{ax / \alpha_1}} - \tan{ax / \alpha_2} \cdot \tan{bx / \alpha_2} - \frac{A_1 \cdot \tan{bx / \alpha_2}}{\tan{\ax / \alpha_1}} = 1$$

 

[HallsofIvy]

That appears to be a single equation in two different variables, x_a and x_b. It will not have a single solution.

 

[mike79]

x is the only variable. a and b are real constants. you have to read x*a and x*b and not x_{a and xb}

 

[csprof2000]

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'.

 

[mike79]

Exactly