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lny=-2ln(x^2+1)+const la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
                / 2    \    
log(y) = - 2*log\x  + 1/ + c
log⁡(y)=c−2log⁡(x2+1)\log{\left(y \right)} = c - 2 \log{\left(x^{2} + 1 \right)}
Simplificar
Gráfica
Respuesta rápida [src] 
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             /   |       |   - ||       |   - |     |atan2|im|-----|, -1 + re|-----|||           /   |       |   - ||       |   - |     |atan2|im|-----|, -1 + re|-----|||
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x1 = -    /      |-1 + re|-----||  + im |-----| *cos|--------------------------------| - I*   /      |-1 + re|-----||  + im |-----| *sin|--------------------------------|
       4 /       |       |  ___||       |  ___|     \               2                /     4 /       |       |  ___||       |  ___|     \               2                /
       \/        \       \\/ y //       \\/ y /                                            \/        \       \\/ y //       \\/ y /
x1=−i(re⁡(ec2y)−1)2+(im⁡(ec2y))24sin⁡(atan2⁡(im⁡(ec2y),re⁡(ec2y)−1)2)−(re⁡(ec2y)−1)2+(im⁡(ec2y))24cos⁡(atan2⁡(im⁡(ec2y),re⁡(ec2y)−1)2)x_{1} = - i \sqrt[4]{\left(\operatorname{re}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)},\operatorname{re}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)} - 1 \right)}}{2} \right)} - \sqrt[4]{\left(\operatorname{re}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)},\operatorname{re}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)} - 1 \right)}}{2} \right)} 
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           /   |       |   - ||       |   - |     |atan2|im|-----|, -1 + re|-----|||           /   |       |   - ||       |   - |     |atan2|im|-----|, -1 + re|-----|||
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x2 =    /      |-1 + re|-----||  + im |-----| *cos|--------------------------------| + I*   /      |-1 + re|-----||  + im |-----| *sin|--------------------------------|
     4 /       |       |  ___||       |  ___|     \               2                /     4 /       |       |  ___||       |  ___|     \               2                /
     \/        \       \\/ y //       \\/ y /                                            \/        \       \\/ y //       \\/ y /
x2=i(re⁡(ec2y)−1)2+(im⁡(ec2y))24sin⁡(atan2⁡(im⁡(ec2y),re⁡(ec2y)−1)2)+(re⁡(ec2y)−1)2+(im⁡(ec2y))24cos⁡(atan2⁡(im⁡(ec2y),re⁡(ec2y)−1)2)x_{2} = i \sqrt[4]{\left(\operatorname{re}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)},\operatorname{re}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)} - 1 \right)}}{2} \right)} + \sqrt[4]{\left(\operatorname{re}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)},\operatorname{re}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)} - 1 \right)}}{2} \right)} 
x2 = i*((re(exp(c/2)/sqrt(y)) - 1)^2 + im(exp(c/2)/sqrt(y))^2)^(1/4)*sin(atan2(im(exp(c/2)/sqrt(y), re(exp(c/2)/sqrt(y)) - 1)/2) + ((re(exp(c/2)/sqrt(y)) - 1)^2 + im(exp(c/2)/sqrt(y))^2)^(1/4)*cos(atan2(im(exp(c/2)/sqrt(y)), re(exp(c/2)/sqrt(y)) - 1)/2))
Suma y producto de raíces [src] 
suma
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           ________________________________    |     |  |   - |         |   - |||              ________________________________    |     |  |   - |         |   - |||            ________________________________    |     |  |   - |         |   - |||              ________________________________    |     |  |   - |         |   - |||
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        /   |       |   - ||       |   - |     |atan2|im|-----|, -1 + re|-----|||           /   |       |   - ||       |   - |     |atan2|im|-----|, -1 + re|-----|||         /   |       |   - ||       |   - |     |atan2|im|-----|, -1 + re|-----|||           /   |       |   - ||       |   - |     |atan2|im|-----|, -1 + re|-----|||
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      /     |       |  e  ||      2|  e  |     |     \  \\/ y /         \\/ y //|         /     |       |  e  ||      2|  e  |     |     \  \\/ y /         \\/ y //|       /     |       |  e  ||      2|  e  |     |     \  \\/ y /         \\/ y //|         /     |       |  e  ||      2|  e  |     |     \  \\/ y /         \\/ y //|
-    /      |-1 + re|-----||  + im |-----| *cos|--------------------------------| - I*   /      |-1 + re|-----||  + im |-----| *sin|--------------------------------| +    /      |-1 + re|-----||  + im |-----| *cos|--------------------------------| + I*   /      |-1 + re|-----||  + im |-----| *sin|--------------------------------|
  4 /       |       |  ___||       |  ___|     \               2                /     4 /       |       |  ___||       |  ___|     \               2                /   4 /       |       |  ___||       |  ___|     \               2                /     4 /       |       |  ___||       |  ___|     \               2                /
  \/        \       \\/ y //       \\/ y /                                            \/        \       \\/ y //       \\/ y /                                          \/        \       \\/ y //       \\/ y /                                            \/        \       \\/ y //       \\/ y /
(−i(re⁡(ec2y)−1)2+(im⁡(ec2y))24sin⁡(atan2⁡(im⁡(ec2y),re⁡(ec2y)−1)2)−(re⁡(ec2y)−1)2+(im⁡(ec2y))24cos⁡(atan2⁡(im⁡(ec2y),re⁡(ec2y)−1)2))+(i(re⁡(ec2y)−1)2+(im⁡(ec2y))24sin⁡(atan2⁡(im⁡(ec2y),re⁡(ec2y)−1)2)+(re⁡(ec2y)−1)2+(im⁡(ec2y))24cos⁡(atan2⁡(im⁡(ec2y),re⁡(ec2y)−1)2))\left(- i \sqrt[4]{\left(\operatorname{re}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)},\operatorname{re}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)} - 1 \right)}}{2} \right)} - \sqrt[4]{\left(\operatorname{re}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)},\operatorname{re}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)} - 1 \right)}}{2} \right)}\right) + \left(i \sqrt[4]{\left(\operatorname{re}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)},\operatorname{re}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)} - 1 \right)}}{2} \right)} + \sqrt[4]{\left(\operatorname{re}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)},\operatorname{re}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)} - 1 \right)}}{2} \right)}\right) 
=
0
00 
producto
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|           ________________________________    |     |  |   - |         |   - |||              ________________________________    |     |  |   - |         |   - |||| |         ________________________________    |     |  |   - |         |   - |||              ________________________________    |     |  |   - |         |   - ||||
|          /                 2                  |     |  |   2 |         |   2 |||             /                 2                  |     |  |   2 |         |   2 |||| |        /                 2                  |     |  |   2 |         |   2 |||             /                 2                  |     |  |   2 |         |   2 ||||
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|        /   |       |   - ||       |   - |     |atan2|im|-----|, -1 + re|-----|||           /   |       |   - ||       |   - |     |atan2|im|-----|, -1 + re|-----|||| |      /   |       |   - ||       |   - |     |atan2|im|-----|, -1 + re|-----|||           /   |       |   - ||       |   - |     |atan2|im|-----|, -1 + re|-----||||
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|      /     |       |  e  ||      2|  e  |     |     \  \\/ y /         \\/ y //|         /     |       |  e  ||      2|  e  |     |     \  \\/ y /         \\/ y //|| |    /     |       |  e  ||      2|  e  |     |     \  \\/ y /         \\/ y //|         /     |       |  e  ||      2|  e  |     |     \  \\/ y /         \\/ y //||
|-    /      |-1 + re|-----||  + im |-----| *cos|--------------------------------| - I*   /      |-1 + re|-----||  + im |-----| *sin|--------------------------------||*|   /      |-1 + re|-----||  + im |-----| *cos|--------------------------------| + I*   /      |-1 + re|-----||  + im |-----| *sin|--------------------------------||
|  4 /       |       |  ___||       |  ___|     \               2                /     4 /       |       |  ___||       |  ___|     \               2                /| |4 /       |       |  ___||       |  ___|     \               2                /     4 /       |       |  ___||       |  ___|     \               2                /|
\  \/        \       \\/ y //       \\/ y /                                            \/        \       \\/ y //       \\/ y /                                       / \\/        \       \\/ y //       \\/ y /                                            \/        \       \\/ y //       \\/ y /                                       /
(−i(re⁡(ec2y)−1)2+(im⁡(ec2y))24sin⁡(atan2⁡(im⁡(ec2y),re⁡(ec2y)−1)2)−(re⁡(ec2y)−1)2+(im⁡(ec2y))24cos⁡(atan2⁡(im⁡(ec2y),re⁡(ec2y)−1)2))(i(re⁡(ec2y)−1)2+(im⁡(ec2y))24sin⁡(atan2⁡(im⁡(ec2y),re⁡(ec2y)−1)2)+(re⁡(ec2y)−1)2+(im⁡(ec2y))24cos⁡(atan2⁡(im⁡(ec2y),re⁡(ec2y)−1)2))\left(- i \sqrt[4]{\left(\operatorname{re}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)},\operatorname{re}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)} - 1 \right)}}{2} \right)} - \sqrt[4]{\left(\operatorname{re}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)},\operatorname{re}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)} - 1 \right)}}{2} \right)}\right) \left(i \sqrt[4]{\left(\operatorname{re}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)},\operatorname{re}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)} - 1 \right)}}{2} \right)} + \sqrt[4]{\left(\operatorname{re}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)},\operatorname{re}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)} - 1 \right)}}{2} \right)}\right) 
=
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       /   |       |   - ||       |   - |   I*atan2|im|-----|, -1 + re|-----||
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-   /      |-1 + re|-----||  + im |-----| *e                                  
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 \/        \       \\/ y //       \\/ y /
−(re⁡(ec2y)−1)2+(im⁡(ec2y))2eiatan2⁡(im⁡(ec2y),re⁡(ec2y)−1)- \sqrt{\left(\operatorname{re}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)}\right)^{2}} e^{i \operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)},\operatorname{re}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)} - 1 \right)}} 
-sqrt((-1 + re(exp(c/2)/sqrt(y)))^2 + im(exp(c/2)/sqrt(y))^2)*exp(i*atan2(im(exp(c/2)/sqrt(y)), -1 + re(exp(c/2)/sqrt(y))))
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