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y^2=x+(lny)/x la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
 2       log(y)
y  = x + ------
           x
y2=x+log⁡(y)xy^{2} = x + \frac{\log{\left(y \right)}}{x}
Simplificar
Gráfica
Respuesta rápida [src] 
                                                                  / /          2\\                          / /          2\\                                        
                                                                  | |      -2*x ||                          | |      -2*x ||                                        
        /  / /          2\\                \    2        2      re\W\-2*x*e     //        2        2      re\W\-2*x*e     //    /  / /          2\\                \
        |  | |      -2*x ||                |  im (x) - re (x) - ------------------      im (x) - re (x) - ------------------    |  | |      -2*x ||                |
        |im\W\-2*x*e     //                |                            2                                         2             |im\W\-2*x*e     //                |
y1 = cos|------------------ + 2*im(x)*re(x)|*e                                     - I*e                                    *sin|------------------ + 2*im(x)*re(x)|
        \        2                         /                                                                                    \        2                         /
y1=−ie−(re⁡(x))2−re⁡(W(−2xe−2x2))2+(im⁡(x))2sin⁡(2re⁡(x)im⁡(x)+im⁡(W(−2xe−2x2))2)+e−(re⁡(x))2−re⁡(W(−2xe−2x2))2+(im⁡(x))2cos⁡(2re⁡(x)im⁡(x)+im⁡(W(−2xe−2x2))2)y_{1} = - i e^{- \left(\operatorname{re}{\left(x\right)}\right)^{2} - \frac{\operatorname{re}{\left(W\left(- 2 x e^{- 2 x^{2}}\right)\right)}}{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + \frac{\operatorname{im}{\left(W\left(- 2 x e^{- 2 x^{2}}\right)\right)}}{2} \right)} + e^{- \left(\operatorname{re}{\left(x\right)}\right)^{2} - \frac{\operatorname{re}{\left(W\left(- 2 x e^{- 2 x^{2}}\right)\right)}}{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + \frac{\operatorname{im}{\left(W\left(- 2 x e^{- 2 x^{2}}\right)\right)}}{2} \right)} 
y1 = -i*exp(-re(x)^2 - re(LambertW(-2*x*exp(-2*x^2)))/2 + im(x)^2)*sin(2*re(x)*im(x) + im(LambertW(-2*x*exp(-2*x^2)))/2) + exp(-re(x)^2 - re(LambertW(-2*x*exp(-2*x^2)))/2 + im(x)^2)*cos(2*re(x)*im(x) + im(LambertW(-2*x*exp(-2*x^2)))/2)
Suma y producto de raíces [src] 
suma
                                                             / /          2\\                          / /          2\\                                        
                                                             | |      -2*x ||                          | |      -2*x ||                                        
   /  / /          2\\                \    2        2      re\W\-2*x*e     //        2        2      re\W\-2*x*e     //    /  / /          2\\                \
   |  | |      -2*x ||                |  im (x) - re (x) - ------------------      im (x) - re (x) - ------------------    |  | |      -2*x ||                |
   |im\W\-2*x*e     //                |                            2                                         2             |im\W\-2*x*e     //                |
cos|------------------ + 2*im(x)*re(x)|*e                                     - I*e                                    *sin|------------------ + 2*im(x)*re(x)|
   \        2                         /                                                                                    \        2                         /
−ie−(re⁡(x))2−re⁡(W(−2xe−2x2))2+(im⁡(x))2sin⁡(2re⁡(x)im⁡(x)+im⁡(W(−2xe−2x2))2)+e−(re⁡(x))2−re⁡(W(−2xe−2x2))2+(im⁡(x))2cos⁡(2re⁡(x)im⁡(x)+im⁡(W(−2xe−2x2))2)- i e^{- \left(\operatorname{re}{\left(x\right)}\right)^{2} - \frac{\operatorname{re}{\left(W\left(- 2 x e^{- 2 x^{2}}\right)\right)}}{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + \frac{\operatorname{im}{\left(W\left(- 2 x e^{- 2 x^{2}}\right)\right)}}{2} \right)} + e^{- \left(\operatorname{re}{\left(x\right)}\right)^{2} - \frac{\operatorname{re}{\left(W\left(- 2 x e^{- 2 x^{2}}\right)\right)}}{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + \frac{\operatorname{im}{\left(W\left(- 2 x e^{- 2 x^{2}}\right)\right)}}{2} \right)} 
=
                                                             / /          2\\                          / /          2\\                                        
                                                             | |      -2*x ||                          | |      -2*x ||                                        
   /  / /          2\\                \    2        2      re\W\-2*x*e     //        2        2      re\W\-2*x*e     //    /  / /          2\\                \
   |  | |      -2*x ||                |  im (x) - re (x) - ------------------      im (x) - re (x) - ------------------    |  | |      -2*x ||                |
   |im\W\-2*x*e     //                |                            2                                         2             |im\W\-2*x*e     //                |
cos|------------------ + 2*im(x)*re(x)|*e                                     - I*e                                    *sin|------------------ + 2*im(x)*re(x)|
   \        2                         /                                                                                    \        2                         /
−ie−(re⁡(x))2−re⁡(W(−2xe−2x2))2+(im⁡(x))2sin⁡(2re⁡(x)im⁡(x)+im⁡(W(−2xe−2x2))2)+e−(re⁡(x))2−re⁡(W(−2xe−2x2))2+(im⁡(x))2cos⁡(2re⁡(x)im⁡(x)+im⁡(W(−2xe−2x2))2)- i e^{- \left(\operatorname{re}{\left(x\right)}\right)^{2} - \frac{\operatorname{re}{\left(W\left(- 2 x e^{- 2 x^{2}}\right)\right)}}{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + \frac{\operatorname{im}{\left(W\left(- 2 x e^{- 2 x^{2}}\right)\right)}}{2} \right)} + e^{- \left(\operatorname{re}{\left(x\right)}\right)^{2} - \frac{\operatorname{re}{\left(W\left(- 2 x e^{- 2 x^{2}}\right)\right)}}{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + \frac{\operatorname{im}{\left(W\left(- 2 x e^{- 2 x^{2}}\right)\right)}}{2} \right)} 
producto
                                                             / /          2\\                          / /          2\\                                        
                                                             | |      -2*x ||                          | |      -2*x ||                                        
   /  / /          2\\                \    2        2      re\W\-2*x*e     //        2        2      re\W\-2*x*e     //    /  / /          2\\                \
   |  | |      -2*x ||                |  im (x) - re (x) - ------------------      im (x) - re (x) - ------------------    |  | |      -2*x ||                |
   |im\W\-2*x*e     //                |                            2                                         2             |im\W\-2*x*e     //                |
cos|------------------ + 2*im(x)*re(x)|*e                                     - I*e                                    *sin|------------------ + 2*im(x)*re(x)|
   \        2                         /                                                                                    \        2                         /
−ie−(re⁡(x))2−re⁡(W(−2xe−2x2))2+(im⁡(x))2sin⁡(2re⁡(x)im⁡(x)+im⁡(W(−2xe−2x2))2)+e−(re⁡(x))2−re⁡(W(−2xe−2x2))2+(im⁡(x))2cos⁡(2re⁡(x)im⁡(x)+im⁡(W(−2xe−2x2))2)- i e^{- \left(\operatorname{re}{\left(x\right)}\right)^{2} - \frac{\operatorname{re}{\left(W\left(- 2 x e^{- 2 x^{2}}\right)\right)}}{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + \frac{\operatorname{im}{\left(W\left(- 2 x e^{- 2 x^{2}}\right)\right)}}{2} \right)} + e^{- \left(\operatorname{re}{\left(x\right)}\right)^{2} - \frac{\operatorname{re}{\left(W\left(- 2 x e^{- 2 x^{2}}\right)\right)}}{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + \frac{\operatorname{im}{\left(W\left(- 2 x e^{- 2 x^{2}}\right)\right)}}{2} \right)} 
=
                     / /          2\\     /    / /          2\\                \
                     | |      -2*x ||     |    | |      -2*x ||                |
   2        2      re\W\-2*x*e     //     |  im\W\-2*x*e     //                |
 im (x) - re (x) - ------------------ + I*|- ------------------ - 2*im(x)*re(x)|
                           2              \          2                         /
e
ei(−2re⁡(x)im⁡(x)−im⁡(W(−2xe−2x2))2)−(re⁡(x))2−re⁡(W(−2xe−2x2))2+(im⁡(x))2e^{i \left(- 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - \frac{\operatorname{im}{\left(W\left(- 2 x e^{- 2 x^{2}}\right)\right)}}{2}\right) - \left(\operatorname{re}{\left(x\right)}\right)^{2} - \frac{\operatorname{re}{\left(W\left(- 2 x e^{- 2 x^{2}}\right)\right)}}{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} 
exp(im(x)^2 - re(x)^2 - re(LambertW(-2*x*exp(-2*x^2)))/2 + i*(-im(LambertW(-2*x*exp(-2*x^2)))/2 - 2*im(x)*re(x)))
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