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x^y-y^x=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
 y    x    
x  - y  = 0
xy−yx=0x^{y} - y^{x} = 0
Simplificar
Gráfica
Respuesta rápida [src] 
         /   /-log(y) \\       /   /-log(y) \\
         |y*W|--------||       |y*W|--------||
         |   \   y    /|       |   \   y    /|
x1 = - re|-------------| - I*im|-------------|
         \    log(y)   /       \    log(y)   /
x1=−re⁡(yW(−log⁡(y)y)log⁡(y))−iim⁡(yW(−log⁡(y)y)log⁡(y))x_{1} = - \operatorname{re}{\left(\frac{y W\left(- \frac{\log{\left(y \right)}}{y}\right)}{\log{\left(y \right)}}\right)} - i \operatorname{im}{\left(\frac{y W\left(- \frac{\log{\left(y \right)}}{y}\right)}{\log{\left(y \right)}}\right)} 
x1 = -re(y*LambertW(-log(y)/y)/log(y)) - i*im(y*LambertW(-log(y)/y)/log(y))
Suma y producto de raíces [src] 
suma
    /   /-log(y) \\       /   /-log(y) \\
    |y*W|--------||       |y*W|--------||
    |   \   y    /|       |   \   y    /|
- re|-------------| - I*im|-------------|
    \    log(y)   /       \    log(y)   /
−re⁡(yW(−log⁡(y)y)log⁡(y))−iim⁡(yW(−log⁡(y)y)log⁡(y))- \operatorname{re}{\left(\frac{y W\left(- \frac{\log{\left(y \right)}}{y}\right)}{\log{\left(y \right)}}\right)} - i \operatorname{im}{\left(\frac{y W\left(- \frac{\log{\left(y \right)}}{y}\right)}{\log{\left(y \right)}}\right)} 
=
    /   /-log(y) \\       /   /-log(y) \\
    |y*W|--------||       |y*W|--------||
    |   \   y    /|       |   \   y    /|
- re|-------------| - I*im|-------------|
    \    log(y)   /       \    log(y)   /
−re⁡(yW(−log⁡(y)y)log⁡(y))−iim⁡(yW(−log⁡(y)y)log⁡(y))- \operatorname{re}{\left(\frac{y W\left(- \frac{\log{\left(y \right)}}{y}\right)}{\log{\left(y \right)}}\right)} - i \operatorname{im}{\left(\frac{y W\left(- \frac{\log{\left(y \right)}}{y}\right)}{\log{\left(y \right)}}\right)} 
producto
    /   /-log(y) \\       /   /-log(y) \\
    |y*W|--------||       |y*W|--------||
    |   \   y    /|       |   \   y    /|
- re|-------------| - I*im|-------------|
    \    log(y)   /       \    log(y)   /
−re⁡(yW(−log⁡(y)y)log⁡(y))−iim⁡(yW(−log⁡(y)y)log⁡(y))- \operatorname{re}{\left(\frac{y W\left(- \frac{\log{\left(y \right)}}{y}\right)}{\log{\left(y \right)}}\right)} - i \operatorname{im}{\left(\frac{y W\left(- \frac{\log{\left(y \right)}}{y}\right)}{\log{\left(y \right)}}\right)} 
=
    /   /-log(y) \\       /   /-log(y) \\
    |y*W|--------||       |y*W|--------||
    |   \   y    /|       |   \   y    /|
- re|-------------| - I*im|-------------|
    \    log(y)   /       \    log(y)   /
−re⁡(yW(−log⁡(y)y)log⁡(y))−iim⁡(yW(−log⁡(y)y)log⁡(y))- \operatorname{re}{\left(\frac{y W\left(- \frac{\log{\left(y \right)}}{y}\right)}{\log{\left(y \right)}}\right)} - i \operatorname{im}{\left(\frac{y W\left(- \frac{\log{\left(y \right)}}{y}\right)}{\log{\left(y \right)}}\right)} 
-re(y*LambertW(-log(y)/y)/log(y)) - i*im(y*LambertW(-log(y)/y)/log(y))
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