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arctg(2x-y)-e^x la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
                 x    
atan(2*x - y) - E  = 0
−ex+atan⁡(2x−y)=0- e^{x} + \operatorname{atan}{\left(2 x - y \right)} = 0
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Gráfica
Respuesta rápida [src] 
                 /                           /   re(x)           \              \                    /              re(x)\              
                 |                       sinh\2*e     *sin(im(x))/              |                 sin\2*cos(im(x))*e     /              
y1 = 2*re(x) + I*|2*im(x) - ----------------------------------------------------| - ----------------------------------------------------
                 |             /              re(x)\       /   re(x)           \|      /              re(x)\       /   re(x)           \
                 \          cos\2*cos(im(x))*e     / + cosh\2*e     *sin(im(x))//   cos\2*cos(im(x))*e     / + cosh\2*e     *sin(im(x))/
y1=i(2im⁡(x)−sinh⁡(2ere⁡(x)sin⁡(im⁡(x)))cos⁡(2ere⁡(x)cos⁡(im⁡(x)))+cosh⁡(2ere⁡(x)sin⁡(im⁡(x))))+2re⁡(x)−sin⁡(2ere⁡(x)cos⁡(im⁡(x)))cos⁡(2ere⁡(x)cos⁡(im⁡(x)))+cosh⁡(2ere⁡(x)sin⁡(im⁡(x)))y_{1} = i \left(2 \operatorname{im}{\left(x\right)} - \frac{\sinh{\left(2 e^{\operatorname{re}{\left(x\right)}} \sin{\left(\operatorname{im}{\left(x\right)} \right)} \right)}}{\cos{\left(2 e^{\operatorname{re}{\left(x\right)}} \cos{\left(\operatorname{im}{\left(x\right)} \right)} \right)} + \cosh{\left(2 e^{\operatorname{re}{\left(x\right)}} \sin{\left(\operatorname{im}{\left(x\right)} \right)} \right)}}\right) + 2 \operatorname{re}{\left(x\right)} - \frac{\sin{\left(2 e^{\operatorname{re}{\left(x\right)}} \cos{\left(\operatorname{im}{\left(x\right)} \right)} \right)}}{\cos{\left(2 e^{\operatorname{re}{\left(x\right)}} \cos{\left(\operatorname{im}{\left(x\right)} \right)} \right)} + \cosh{\left(2 e^{\operatorname{re}{\left(x\right)}} \sin{\left(\operatorname{im}{\left(x\right)} \right)} \right)}} 
y1 = i*(2*im(x) - sinh(2*exp(re(x))*sin(im(x)))/(cos(2*exp(re(x))*cos(im(x))) + cosh(2*exp(re(x))*sin(im(x))))) + 2*re(x) - sin(2*exp(re(x))*cos(im(x)))/(cos(2*exp(re(x))*cos(im(x))) + cosh(2*exp(re(x))*sin(im(x))))
Suma y producto de raíces [src] 
suma
            /                           /   re(x)           \              \                    /              re(x)\              
            |                       sinh\2*e     *sin(im(x))/              |                 sin\2*cos(im(x))*e     /              
2*re(x) + I*|2*im(x) - ----------------------------------------------------| - ----------------------------------------------------
            |             /              re(x)\       /   re(x)           \|      /              re(x)\       /   re(x)           \
            \          cos\2*cos(im(x))*e     / + cosh\2*e     *sin(im(x))//   cos\2*cos(im(x))*e     / + cosh\2*e     *sin(im(x))/
i(2im⁡(x)−sinh⁡(2ere⁡(x)sin⁡(im⁡(x)))cos⁡(2ere⁡(x)cos⁡(im⁡(x)))+cosh⁡(2ere⁡(x)sin⁡(im⁡(x))))+2re⁡(x)−sin⁡(2ere⁡(x)cos⁡(im⁡(x)))cos⁡(2ere⁡(x)cos⁡(im⁡(x)))+cosh⁡(2ere⁡(x)sin⁡(im⁡(x)))i \left(2 \operatorname{im}{\left(x\right)} - \frac{\sinh{\left(2 e^{\operatorname{re}{\left(x\right)}} \sin{\left(\operatorname{im}{\left(x\right)} \right)} \right)}}{\cos{\left(2 e^{\operatorname{re}{\left(x\right)}} \cos{\left(\operatorname{im}{\left(x\right)} \right)} \right)} + \cosh{\left(2 e^{\operatorname{re}{\left(x\right)}} \sin{\left(\operatorname{im}{\left(x\right)} \right)} \right)}}\right) + 2 \operatorname{re}{\left(x\right)} - \frac{\sin{\left(2 e^{\operatorname{re}{\left(x\right)}} \cos{\left(\operatorname{im}{\left(x\right)} \right)} \right)}}{\cos{\left(2 e^{\operatorname{re}{\left(x\right)}} \cos{\left(\operatorname{im}{\left(x\right)} \right)} \right)} + \cosh{\left(2 e^{\operatorname{re}{\left(x\right)}} \sin{\left(\operatorname{im}{\left(x\right)} \right)} \right)}} 
=
            /                           /   re(x)           \              \                    /              re(x)\              
            |                       sinh\2*e     *sin(im(x))/              |                 sin\2*cos(im(x))*e     /              
2*re(x) + I*|2*im(x) - ----------------------------------------------------| - ----------------------------------------------------
            |             /              re(x)\       /   re(x)           \|      /              re(x)\       /   re(x)           \
            \          cos\2*cos(im(x))*e     / + cosh\2*e     *sin(im(x))//   cos\2*cos(im(x))*e     / + cosh\2*e     *sin(im(x))/
i(2im⁡(x)−sinh⁡(2ere⁡(x)sin⁡(im⁡(x)))cos⁡(2ere⁡(x)cos⁡(im⁡(x)))+cosh⁡(2ere⁡(x)sin⁡(im⁡(x))))+2re⁡(x)−sin⁡(2ere⁡(x)cos⁡(im⁡(x)))cos⁡(2ere⁡(x)cos⁡(im⁡(x)))+cosh⁡(2ere⁡(x)sin⁡(im⁡(x)))i \left(2 \operatorname{im}{\left(x\right)} - \frac{\sinh{\left(2 e^{\operatorname{re}{\left(x\right)}} \sin{\left(\operatorname{im}{\left(x\right)} \right)} \right)}}{\cos{\left(2 e^{\operatorname{re}{\left(x\right)}} \cos{\left(\operatorname{im}{\left(x\right)} \right)} \right)} + \cosh{\left(2 e^{\operatorname{re}{\left(x\right)}} \sin{\left(\operatorname{im}{\left(x\right)} \right)} \right)}}\right) + 2 \operatorname{re}{\left(x\right)} - \frac{\sin{\left(2 e^{\operatorname{re}{\left(x\right)}} \cos{\left(\operatorname{im}{\left(x\right)} \right)} \right)}}{\cos{\left(2 e^{\operatorname{re}{\left(x\right)}} \cos{\left(\operatorname{im}{\left(x\right)} \right)} \right)} + \cosh{\left(2 e^{\operatorname{re}{\left(x\right)}} \sin{\left(\operatorname{im}{\left(x\right)} \right)} \right)}} 
producto
            /                           /   re(x)           \              \                    /              re(x)\              
            |                       sinh\2*e     *sin(im(x))/              |                 sin\2*cos(im(x))*e     /              
2*re(x) + I*|2*im(x) - ----------------------------------------------------| - ----------------------------------------------------
            |             /              re(x)\       /   re(x)           \|      /              re(x)\       /   re(x)           \
            \          cos\2*cos(im(x))*e     / + cosh\2*e     *sin(im(x))//   cos\2*cos(im(x))*e     / + cosh\2*e     *sin(im(x))/
i(2im⁡(x)−sinh⁡(2ere⁡(x)sin⁡(im⁡(x)))cos⁡(2ere⁡(x)cos⁡(im⁡(x)))+cosh⁡(2ere⁡(x)sin⁡(im⁡(x))))+2re⁡(x)−sin⁡(2ere⁡(x)cos⁡(im⁡(x)))cos⁡(2ere⁡(x)cos⁡(im⁡(x)))+cosh⁡(2ere⁡(x)sin⁡(im⁡(x)))i \left(2 \operatorname{im}{\left(x\right)} - \frac{\sinh{\left(2 e^{\operatorname{re}{\left(x\right)}} \sin{\left(\operatorname{im}{\left(x\right)} \right)} \right)}}{\cos{\left(2 e^{\operatorname{re}{\left(x\right)}} \cos{\left(\operatorname{im}{\left(x\right)} \right)} \right)} + \cosh{\left(2 e^{\operatorname{re}{\left(x\right)}} \sin{\left(\operatorname{im}{\left(x\right)} \right)} \right)}}\right) + 2 \operatorname{re}{\left(x\right)} - \frac{\sin{\left(2 e^{\operatorname{re}{\left(x\right)}} \cos{\left(\operatorname{im}{\left(x\right)} \right)} \right)}}{\cos{\left(2 e^{\operatorname{re}{\left(x\right)}} \cos{\left(\operatorname{im}{\left(x\right)} \right)} \right)} + \cosh{\left(2 e^{\operatorname{re}{\left(x\right)}} \sin{\left(\operatorname{im}{\left(x\right)} \right)} \right)}} 
=
     /              re(x)\     /      /   re(x)           \     /   /              re(x)\       /   re(x)           \\      \     /   /              re(x)\       /   re(x)           \\      
- sin\2*cos(im(x))*e     / + I*\- sinh\2*e     *sin(im(x))/ + 2*\cos\2*cos(im(x))*e     / + cosh\2*e     *sin(im(x))//*im(x)/ + 2*\cos\2*cos(im(x))*e     / + cosh\2*e     *sin(im(x))//*re(x)
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                        /              re(x)\       /   re(x)           \                                                                     
                                                                     cos\2*cos(im(x))*e     / + cosh\2*e     *sin(im(x))/
i(2(cos⁡(2ere⁡(x)cos⁡(im⁡(x)))+cosh⁡(2ere⁡(x)sin⁡(im⁡(x))))im⁡(x)−sinh⁡(2ere⁡(x)sin⁡(im⁡(x))))+2(cos⁡(2ere⁡(x)cos⁡(im⁡(x)))+cosh⁡(2ere⁡(x)sin⁡(im⁡(x))))re⁡(x)−sin⁡(2ere⁡(x)cos⁡(im⁡(x)))cos⁡(2ere⁡(x)cos⁡(im⁡(x)))+cosh⁡(2ere⁡(x)sin⁡(im⁡(x)))\frac{i \left(2 \left(\cos{\left(2 e^{\operatorname{re}{\left(x\right)}} \cos{\left(\operatorname{im}{\left(x\right)} \right)} \right)} + \cosh{\left(2 e^{\operatorname{re}{\left(x\right)}} \sin{\left(\operatorname{im}{\left(x\right)} \right)} \right)}\right) \operatorname{im}{\left(x\right)} - \sinh{\left(2 e^{\operatorname{re}{\left(x\right)}} \sin{\left(\operatorname{im}{\left(x\right)} \right)} \right)}\right) + 2 \left(\cos{\left(2 e^{\operatorname{re}{\left(x\right)}} \cos{\left(\operatorname{im}{\left(x\right)} \right)} \right)} + \cosh{\left(2 e^{\operatorname{re}{\left(x\right)}} \sin{\left(\operatorname{im}{\left(x\right)} \right)} \right)}\right) \operatorname{re}{\left(x\right)} - \sin{\left(2 e^{\operatorname{re}{\left(x\right)}} \cos{\left(\operatorname{im}{\left(x\right)} \right)} \right)}}{\cos{\left(2 e^{\operatorname{re}{\left(x\right)}} \cos{\left(\operatorname{im}{\left(x\right)} \right)} \right)} + \cosh{\left(2 e^{\operatorname{re}{\left(x\right)}} \sin{\left(\operatorname{im}{\left(x\right)} \right)} \right)}} 
(-sin(2*cos(im(x))*exp(re(x))) + i*(-sinh(2*exp(re(x))*sin(im(x))) + 2*(cos(2*cos(im(x))*exp(re(x))) + cosh(2*exp(re(x))*sin(im(x))))*im(x)) + 2*(cos(2*cos(im(x))*exp(re(x))) + cosh(2*exp(re(x))*sin(im(x))))*re(x))/(cos(2*cos(im(x))*exp(re(x))) + cosh(2*exp(re(x))*sin(im(x))))
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