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xy+e^(x+y)+4=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
       x + y        
x*y + E      + 4 = 0
(ex+y+xy)+4=0\left(e^{x + y} + x y\right) + 4 = 0
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Gráfica
Respuesta rápida [src] 
         / /     4\\     /    / /     4\\                  \                  
         | | x - -||     |    | | x - -||                  |                  
         | |     x||     |    | |     x||                  |                  
         | |e     ||     |    | |e     ||       4*im(x)    |       4*re(x)    
y1 = - re|W|------|| + I*|- im|W|------|| + ---------------| - ---------------
         \ \  x   //     |    \ \  x   //     2        2   |     2        2   
                         \                  im (x) + re (x)/   im (x) + re (x)
y1=i(−im⁡(W(ex−4xx))+4im⁡(x)(re⁡(x))2+(im⁡(x))2)−re⁡(W(ex−4xx))−4re⁡(x)(re⁡(x))2+(im⁡(x))2y_{1} = i \left(- \operatorname{im}{\left(W\left(\frac{e^{x - \frac{4}{x}}}{x}\right)\right)} + \frac{4 \operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right) - \operatorname{re}{\left(W\left(\frac{e^{x - \frac{4}{x}}}{x}\right)\right)} - \frac{4 \operatorname{re}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} 
y1 = i*(-im(LambertW(exp(x - 4/x)/x)) + 4*im(x)/(re(x)^2 + im(x)^2)) - re(LambertW(exp(x - 4/x)/x)) - 4*re(x)/(re(x)^2 + im(x)^2)
Suma y producto de raíces [src] 
suma
    / /     4\\     /    / /     4\\                  \                  
    | | x - -||     |    | | x - -||                  |                  
    | |     x||     |    | |     x||                  |                  
    | |e     ||     |    | |e     ||       4*im(x)    |       4*re(x)    
- re|W|------|| + I*|- im|W|------|| + ---------------| - ---------------
    \ \  x   //     |    \ \  x   //     2        2   |     2        2   
                    \                  im (x) + re (x)/   im (x) + re (x)
i(−im⁡(W(ex−4xx))+4im⁡(x)(re⁡(x))2+(im⁡(x))2)−re⁡(W(ex−4xx))−4re⁡(x)(re⁡(x))2+(im⁡(x))2i \left(- \operatorname{im}{\left(W\left(\frac{e^{x - \frac{4}{x}}}{x}\right)\right)} + \frac{4 \operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right) - \operatorname{re}{\left(W\left(\frac{e^{x - \frac{4}{x}}}{x}\right)\right)} - \frac{4 \operatorname{re}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} 
=
    / /     4\\     /    / /     4\\                  \                  
    | | x - -||     |    | | x - -||                  |                  
    | |     x||     |    | |     x||                  |                  
    | |e     ||     |    | |e     ||       4*im(x)    |       4*re(x)    
- re|W|------|| + I*|- im|W|------|| + ---------------| - ---------------
    \ \  x   //     |    \ \  x   //     2        2   |     2        2   
                    \                  im (x) + re (x)/   im (x) + re (x)
i(−im⁡(W(ex−4xx))+4im⁡(x)(re⁡(x))2+(im⁡(x))2)−re⁡(W(ex−4xx))−4re⁡(x)(re⁡(x))2+(im⁡(x))2i \left(- \operatorname{im}{\left(W\left(\frac{e^{x - \frac{4}{x}}}{x}\right)\right)} + \frac{4 \operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right) - \operatorname{re}{\left(W\left(\frac{e^{x - \frac{4}{x}}}{x}\right)\right)} - \frac{4 \operatorname{re}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} 
producto
    / /     4\\     /    / /     4\\                  \                  
    | | x - -||     |    | | x - -||                  |                  
    | |     x||     |    | |     x||                  |                  
    | |e     ||     |    | |e     ||       4*im(x)    |       4*re(x)    
- re|W|------|| + I*|- im|W|------|| + ---------------| - ---------------
    \ \  x   //     |    \ \  x   //     2        2   |     2        2   
                    \                  im (x) + re (x)/   im (x) + re (x)
i(−im⁡(W(ex−4xx))+4im⁡(x)(re⁡(x))2+(im⁡(x))2)−re⁡(W(ex−4xx))−4re⁡(x)(re⁡(x))2+(im⁡(x))2i \left(- \operatorname{im}{\left(W\left(\frac{e^{x - \frac{4}{x}}}{x}\right)\right)} + \frac{4 \operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right) - \operatorname{re}{\left(W\left(\frac{e^{x - \frac{4}{x}}}{x}\right)\right)} - \frac{4 \operatorname{re}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} 
=
             /                              / /       2\\\                       / /       2\\
             |                              | | -4 + x |||                       | | -4 + x ||
             |                              | | -------|||                       | | -------||
             |                              | |    x   |||                       | |    x   ||
             |          /  2        2   \   | |e       |||   /  2        2   \   | |e       ||
-4*re(x) + I*|4*im(x) - \im (x) + re (x)/*im|W|--------||| - \im (x) + re (x)/*re|W|--------||
             \                              \ \   x    ///                       \ \   x    //
----------------------------------------------------------------------------------------------
                                         2        2                                           
                                       im (x) + re (x)
i(−((re⁡(x))2+(im⁡(x))2)im⁡(W(ex2−4xx))+4im⁡(x))−((re⁡(x))2+(im⁡(x))2)re⁡(W(ex2−4xx))−4re⁡(x)(re⁡(x))2+(im⁡(x))2\frac{i \left(- \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right) \operatorname{im}{\left(W\left(\frac{e^{\frac{x^{2} - 4}{x}}}{x}\right)\right)} + 4 \operatorname{im}{\left(x\right)}\right) - \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right) \operatorname{re}{\left(W\left(\frac{e^{\frac{x^{2} - 4}{x}}}{x}\right)\right)} - 4 \operatorname{re}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} 
(-4*re(x) + i*(4*im(x) - (im(x)^2 + re(x)^2)*im(LambertW(exp((-4 + x^2)/x)/x))) - (im(x)^2 + re(x)^2)*re(LambertW(exp((-4 + x^2)/x)/x)))/(im(x)^2 + re(x)^2)
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