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atan(x)-1/3*x3=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
          x3    
atan(x) - -- = 0
          3     
$$- \frac{x_{3}}{3} + \operatorname{atan}{\left(x \right)} = 0$$
Gráfica
Suma y producto de raíces [src]
suma
           /2*re(x3)\                         /2*im(x3)\       
        sin|--------|                   I*sinh|--------|       
           \   3    /                         \   3    /       
------------------------------ + ------------------------------
   /2*re(x3)\       /2*im(x3)\      /2*re(x3)\       /2*im(x3)\
cos|--------| + cosh|--------|   cos|--------| + cosh|--------|
   \   3    /       \   3    /      \   3    /       \   3    /
$$\frac{\sin{\left(\frac{2 \operatorname{re}{\left(x_{3}\right)}}{3} \right)}}{\cos{\left(\frac{2 \operatorname{re}{\left(x_{3}\right)}}{3} \right)} + \cosh{\left(\frac{2 \operatorname{im}{\left(x_{3}\right)}}{3} \right)}} + \frac{i \sinh{\left(\frac{2 \operatorname{im}{\left(x_{3}\right)}}{3} \right)}}{\cos{\left(\frac{2 \operatorname{re}{\left(x_{3}\right)}}{3} \right)} + \cosh{\left(\frac{2 \operatorname{im}{\left(x_{3}\right)}}{3} \right)}}$$
=
           /2*re(x3)\                         /2*im(x3)\       
        sin|--------|                   I*sinh|--------|       
           \   3    /                         \   3    /       
------------------------------ + ------------------------------
   /2*re(x3)\       /2*im(x3)\      /2*re(x3)\       /2*im(x3)\
cos|--------| + cosh|--------|   cos|--------| + cosh|--------|
   \   3    /       \   3    /      \   3    /       \   3    /
$$\frac{\sin{\left(\frac{2 \operatorname{re}{\left(x_{3}\right)}}{3} \right)}}{\cos{\left(\frac{2 \operatorname{re}{\left(x_{3}\right)}}{3} \right)} + \cosh{\left(\frac{2 \operatorname{im}{\left(x_{3}\right)}}{3} \right)}} + \frac{i \sinh{\left(\frac{2 \operatorname{im}{\left(x_{3}\right)}}{3} \right)}}{\cos{\left(\frac{2 \operatorname{re}{\left(x_{3}\right)}}{3} \right)} + \cosh{\left(\frac{2 \operatorname{im}{\left(x_{3}\right)}}{3} \right)}}$$
producto
           /2*re(x3)\                         /2*im(x3)\       
        sin|--------|                   I*sinh|--------|       
           \   3    /                         \   3    /       
------------------------------ + ------------------------------
   /2*re(x3)\       /2*im(x3)\      /2*re(x3)\       /2*im(x3)\
cos|--------| + cosh|--------|   cos|--------| + cosh|--------|
   \   3    /       \   3    /      \   3    /       \   3    /
$$\frac{\sin{\left(\frac{2 \operatorname{re}{\left(x_{3}\right)}}{3} \right)}}{\cos{\left(\frac{2 \operatorname{re}{\left(x_{3}\right)}}{3} \right)} + \cosh{\left(\frac{2 \operatorname{im}{\left(x_{3}\right)}}{3} \right)}} + \frac{i \sinh{\left(\frac{2 \operatorname{im}{\left(x_{3}\right)}}{3} \right)}}{\cos{\left(\frac{2 \operatorname{re}{\left(x_{3}\right)}}{3} \right)} + \cosh{\left(\frac{2 \operatorname{im}{\left(x_{3}\right)}}{3} \right)}}$$
=
      /2*im(x3)\      /2*re(x3)\
I*sinh|--------| + sin|--------|
      \   3    /      \   3    /
--------------------------------
    /2*re(x3)\       /2*im(x3)\ 
 cos|--------| + cosh|--------| 
    \   3    /       \   3    / 
$$\frac{\sin{\left(\frac{2 \operatorname{re}{\left(x_{3}\right)}}{3} \right)} + i \sinh{\left(\frac{2 \operatorname{im}{\left(x_{3}\right)}}{3} \right)}}{\cos{\left(\frac{2 \operatorname{re}{\left(x_{3}\right)}}{3} \right)} + \cosh{\left(\frac{2 \operatorname{im}{\left(x_{3}\right)}}{3} \right)}}$$
(i*sinh(2*im(x3)/3) + sin(2*re(x3)/3))/(cos(2*re(x3)/3) + cosh(2*im(x3)/3))
Respuesta rápida [src]
                /2*re(x3)\                         /2*im(x3)\       
             sin|--------|                   I*sinh|--------|       
                \   3    /                         \   3    /       
x1 = ------------------------------ + ------------------------------
        /2*re(x3)\       /2*im(x3)\      /2*re(x3)\       /2*im(x3)\
     cos|--------| + cosh|--------|   cos|--------| + cosh|--------|
        \   3    /       \   3    /      \   3    /       \   3    /
$$x_{1} = \frac{\sin{\left(\frac{2 \operatorname{re}{\left(x_{3}\right)}}{3} \right)}}{\cos{\left(\frac{2 \operatorname{re}{\left(x_{3}\right)}}{3} \right)} + \cosh{\left(\frac{2 \operatorname{im}{\left(x_{3}\right)}}{3} \right)}} + \frac{i \sinh{\left(\frac{2 \operatorname{im}{\left(x_{3}\right)}}{3} \right)}}{\cos{\left(\frac{2 \operatorname{re}{\left(x_{3}\right)}}{3} \right)} + \cosh{\left(\frac{2 \operatorname{im}{\left(x_{3}\right)}}{3} \right)}}$$
x1 = sin(2*re(x3)/3)/(cos(2*re(x3)/3) + cosh(2*im(x3)/3)) + i*sinh(2*im(x3)/3)/(cos(2*re(x3)/3) + cosh(2*im(x3)/3))