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log(y^2+1)/2=c+atan(x) la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
   / 2    \              
log\y  + 1/              
----------- = c + atan(x)
     2
log⁡(y2+1)2=c+atan⁡(x)\frac{\log{\left(y^{2} + 1 \right)}}{2} = c + \operatorname{atan}{\left(x \right)}
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Gráfica
Respuesta rápida [src] 
                        /              /|     2|\\                                        /     /     2\          \               
                     sin\-2*re(c) + log\|1 + y |//                                  I*sinh\- arg\1 + y / + 2*im(c)/               
x1 = ------------------------------------------------------------- - -------------------------------------------------------------
        /              /|     2|\\       /     /     2\          \      /              /|     2|\\       /     /     2\          \
     cos\-2*re(c) + log\|1 + y |// + cosh\- arg\1 + y / + 2*im(c)/   cos\-2*re(c) + log\|1 + y |// + cosh\- arg\1 + y / + 2*im(c)/
x1=sin⁡(log⁡(∣y2+1∣)−2re⁡(c))cos⁡(log⁡(∣y2+1∣)−2re⁡(c))+cosh⁡(2im⁡(c)−arg⁡(y2+1))−isinh⁡(2im⁡(c)−arg⁡(y2+1))cos⁡(log⁡(∣y2+1∣)−2re⁡(c))+cosh⁡(2im⁡(c)−arg⁡(y2+1))x_{1} = \frac{\sin{\left(\log{\left(\left|{y^{2} + 1}\right| \right)} - 2 \operatorname{re}{\left(c\right)} \right)}}{\cos{\left(\log{\left(\left|{y^{2} + 1}\right| \right)} - 2 \operatorname{re}{\left(c\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(c\right)} - \arg{\left(y^{2} + 1 \right)} \right)}} - \frac{i \sinh{\left(2 \operatorname{im}{\left(c\right)} - \arg{\left(y^{2} + 1 \right)} \right)}}{\cos{\left(\log{\left(\left|{y^{2} + 1}\right| \right)} - 2 \operatorname{re}{\left(c\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(c\right)} - \arg{\left(y^{2} + 1 \right)} \right)}} 
x1 = sin(log(|y^2 + 1|) - 2*re(c))/(cos(log(|y^2 + 1|) - 2*re(c)) + cosh(2*im(c) - arg(y^2 + 1))) - i*sinh(2*im(c) - arg(y^2 + 1))/(cos(log(|y^2 + 1|) - 2*re(c)) + cosh(2*im(c) - arg(y^2 + 1)))
Suma y producto de raíces [src] 
suma
                   /              /|     2|\\                                        /     /     2\          \               
                sin\-2*re(c) + log\|1 + y |//                                  I*sinh\- arg\1 + y / + 2*im(c)/               
------------------------------------------------------------- - -------------------------------------------------------------
   /              /|     2|\\       /     /     2\          \      /              /|     2|\\       /     /     2\          \
cos\-2*re(c) + log\|1 + y |// + cosh\- arg\1 + y / + 2*im(c)/   cos\-2*re(c) + log\|1 + y |// + cosh\- arg\1 + y / + 2*im(c)/
sin⁡(log⁡(∣y2+1∣)−2re⁡(c))cos⁡(log⁡(∣y2+1∣)−2re⁡(c))+cosh⁡(2im⁡(c)−arg⁡(y2+1))−isinh⁡(2im⁡(c)−arg⁡(y2+1))cos⁡(log⁡(∣y2+1∣)−2re⁡(c))+cosh⁡(2im⁡(c)−arg⁡(y2+1))\frac{\sin{\left(\log{\left(\left|{y^{2} + 1}\right| \right)} - 2 \operatorname{re}{\left(c\right)} \right)}}{\cos{\left(\log{\left(\left|{y^{2} + 1}\right| \right)} - 2 \operatorname{re}{\left(c\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(c\right)} - \arg{\left(y^{2} + 1 \right)} \right)}} - \frac{i \sinh{\left(2 \operatorname{im}{\left(c\right)} - \arg{\left(y^{2} + 1 \right)} \right)}}{\cos{\left(\log{\left(\left|{y^{2} + 1}\right| \right)} - 2 \operatorname{re}{\left(c\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(c\right)} - \arg{\left(y^{2} + 1 \right)} \right)}} 
=
                   /              /|     2|\\                                        /     /     2\          \               
                sin\-2*re(c) + log\|1 + y |//                                  I*sinh\- arg\1 + y / + 2*im(c)/               
------------------------------------------------------------- - -------------------------------------------------------------
   /              /|     2|\\       /     /     2\          \      /              /|     2|\\       /     /     2\          \
cos\-2*re(c) + log\|1 + y |// + cosh\- arg\1 + y / + 2*im(c)/   cos\-2*re(c) + log\|1 + y |// + cosh\- arg\1 + y / + 2*im(c)/
sin⁡(log⁡(∣y2+1∣)−2re⁡(c))cos⁡(log⁡(∣y2+1∣)−2re⁡(c))+cosh⁡(2im⁡(c)−arg⁡(y2+1))−isinh⁡(2im⁡(c)−arg⁡(y2+1))cos⁡(log⁡(∣y2+1∣)−2re⁡(c))+cosh⁡(2im⁡(c)−arg⁡(y2+1))\frac{\sin{\left(\log{\left(\left|{y^{2} + 1}\right| \right)} - 2 \operatorname{re}{\left(c\right)} \right)}}{\cos{\left(\log{\left(\left|{y^{2} + 1}\right| \right)} - 2 \operatorname{re}{\left(c\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(c\right)} - \arg{\left(y^{2} + 1 \right)} \right)}} - \frac{i \sinh{\left(2 \operatorname{im}{\left(c\right)} - \arg{\left(y^{2} + 1 \right)} \right)}}{\cos{\left(\log{\left(\left|{y^{2} + 1}\right| \right)} - 2 \operatorname{re}{\left(c\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(c\right)} - \arg{\left(y^{2} + 1 \right)} \right)}} 
producto
                   /              /|     2|\\                                        /     /     2\          \               
                sin\-2*re(c) + log\|1 + y |//                                  I*sinh\- arg\1 + y / + 2*im(c)/               
------------------------------------------------------------- - -------------------------------------------------------------
   /              /|     2|\\       /     /     2\          \      /              /|     2|\\       /     /     2\          \
cos\-2*re(c) + log\|1 + y |// + cosh\- arg\1 + y / + 2*im(c)/   cos\-2*re(c) + log\|1 + y |// + cosh\- arg\1 + y / + 2*im(c)/
sin⁡(log⁡(∣y2+1∣)−2re⁡(c))cos⁡(log⁡(∣y2+1∣)−2re⁡(c))+cosh⁡(2im⁡(c)−arg⁡(y2+1))−isinh⁡(2im⁡(c)−arg⁡(y2+1))cos⁡(log⁡(∣y2+1∣)−2re⁡(c))+cosh⁡(2im⁡(c)−arg⁡(y2+1))\frac{\sin{\left(\log{\left(\left|{y^{2} + 1}\right| \right)} - 2 \operatorname{re}{\left(c\right)} \right)}}{\cos{\left(\log{\left(\left|{y^{2} + 1}\right| \right)} - 2 \operatorname{re}{\left(c\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(c\right)} - \arg{\left(y^{2} + 1 \right)} \right)}} - \frac{i \sinh{\left(2 \operatorname{im}{\left(c\right)} - \arg{\left(y^{2} + 1 \right)} \right)}}{\cos{\left(\log{\left(\left|{y^{2} + 1}\right| \right)} - 2 \operatorname{re}{\left(c\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(c\right)} - \arg{\left(y^{2} + 1 \right)} \right)}} 
=
        /     /     2\          \      /              /|     2|\\
- I*sinh\- arg\1 + y / + 2*im(c)/ + sin\-2*re(c) + log\|1 + y |//
-----------------------------------------------------------------
     /              /|     2|\\       /     /     2\          \  
  cos\-2*re(c) + log\|1 + y |// + cosh\- arg\1 + y / + 2*im(c)/
sin⁡(log⁡(∣y2+1∣)−2re⁡(c))−isinh⁡(2im⁡(c)−arg⁡(y2+1))cos⁡(log⁡(∣y2+1∣)−2re⁡(c))+cosh⁡(2im⁡(c)−arg⁡(y2+1))\frac{\sin{\left(\log{\left(\left|{y^{2} + 1}\right| \right)} - 2 \operatorname{re}{\left(c\right)} \right)} - i \sinh{\left(2 \operatorname{im}{\left(c\right)} - \arg{\left(y^{2} + 1 \right)} \right)}}{\cos{\left(\log{\left(\left|{y^{2} + 1}\right| \right)} - 2 \operatorname{re}{\left(c\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(c\right)} - \arg{\left(y^{2} + 1 \right)} \right)}} 
(-i*sinh(-arg(1 + y^2) + 2*im(c)) + sin(-2*re(c) + log(|1 + y^2|)))/(cos(-2*re(c) + log(|1 + y^2|)) + cosh(-arg(1 + y^2) + 2*im(c)))
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