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408,03=(((-2375-774,19313*i)/12)*(-x-1,538))*(e^((-2375-774,19313*i)/12)*(t))+((-2375+774,19313*i)/12)*x*(e^((-2375-774,19313*i)/12)*(t)) la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
                                        -2375 - 774.19313*I                            -2375 - 774.19313*I  
                                        -------------------                            -------------------  
40803   -2375 - 774.19313*I /     769\           12             -2375 + 774.19313*I             12          
----- = -------------------*|-x - ---|*E                   *t + -------------------*x*E                   *t
 100             12         \     500/                                   12
40803100=e−2375−774.19313i12tx−2375+774.19313i12+e−2375−774.19313i12t−2375−774.19313i12(−x−769500)\frac{40803}{100} = e^{\frac{-2375 - 774.19313 i}{12}} t x \frac{-2375 + 774.19313 i}{12} + e^{\frac{-2375 - 774.19313 i}{12}} t \frac{-2375 - 774.19313 i}{12} \left(- x - \frac{769}{500}\right)
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Gráfica
Respuesta rápida [src] 
       /1.04221197690107e-51*(3.09034320354466e+136 + 2.2635212754204e+51*re(t) - 7.37853735174449e+50*im(t))*re(t)   1.04221197690107e-51*(2.71239880701756e+137 - 2.2635212754204e+51*im(t) - 7.37853735174449e+50*re(t))*im(t)\   1.04221197690107e-51*(2.71239880701756e+137 - 2.2635212754204e+51*im(t) - 7.37853735174449e+50*re(t))*re(t)   1.04221197690107e-51*(3.09034320354466e+136 + 2.2635212754204e+51*re(t) - 7.37853735174449e+50*im(t))*im(t)
x1 = I*|----------------------------------------------------------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------| + ----------------------------------------------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------------
       |                                                2        2                                                                                                    2        2                                                 |                                                   2        2                                                                                                    2        2                                                 
       \                                              im (t) + re (t)                                                                                               im (t) + re (t)                                              /                                                 im (t) + re (t)                                                                                               im (t) + re (t)
x1=i(−1.04221197690107⋅10−51(−7.37853735174449⋅1050re⁡(t)−2.2635212754204⋅1051im⁡(t)+2.71239880701756⋅10137)im⁡(t)(re⁡(t))2+(im⁡(t))2+1.04221197690107⋅10−51(2.2635212754204⋅1051re⁡(t)−7.37853735174449⋅1050im⁡(t)+3.09034320354466⋅10136)re⁡(t)(re⁡(t))2+(im⁡(t))2)+1.04221197690107⋅10−51(−7.37853735174449⋅1050re⁡(t)−2.2635212754204⋅1051im⁡(t)+2.71239880701756⋅10137)re⁡(t)(re⁡(t))2+(im⁡(t))2+1.04221197690107⋅10−51(2.2635212754204⋅1051re⁡(t)−7.37853735174449⋅1050im⁡(t)+3.09034320354466⋅10136)im⁡(t)(re⁡(t))2+(im⁡(t))2x_{1} = i \left(- \frac{1.04221197690107 \cdot 10^{-51} \left(- 7.37853735174449 \cdot 10^{50} \operatorname{re}{\left(t\right)} - 2.2635212754204 \cdot 10^{51} \operatorname{im}{\left(t\right)} + 2.71239880701756 \cdot 10^{137}\right) \operatorname{im}{\left(t\right)}}{\left(\operatorname{re}{\left(t\right)}\right)^{2} + \left(\operatorname{im}{\left(t\right)}\right)^{2}} + \frac{1.04221197690107 \cdot 10^{-51} \left(2.2635212754204 \cdot 10^{51} \operatorname{re}{\left(t\right)} - 7.37853735174449 \cdot 10^{50} \operatorname{im}{\left(t\right)} + 3.09034320354466 \cdot 10^{136}\right) \operatorname{re}{\left(t\right)}}{\left(\operatorname{re}{\left(t\right)}\right)^{2} + \left(\operatorname{im}{\left(t\right)}\right)^{2}}\right) + \frac{1.04221197690107 \cdot 10^{-51} \left(- 7.37853735174449 \cdot 10^{50} \operatorname{re}{\left(t\right)} - 2.2635212754204 \cdot 10^{51} \operatorname{im}{\left(t\right)} + 2.71239880701756 \cdot 10^{137}\right) \operatorname{re}{\left(t\right)}}{\left(\operatorname{re}{\left(t\right)}\right)^{2} + \left(\operatorname{im}{\left(t\right)}\right)^{2}} + \frac{1.04221197690107 \cdot 10^{-51} \left(2.2635212754204 \cdot 10^{51} \operatorname{re}{\left(t\right)} - 7.37853735174449 \cdot 10^{50} \operatorname{im}{\left(t\right)} + 3.09034320354466 \cdot 10^{136}\right) \operatorname{im}{\left(t\right)}}{\left(\operatorname{re}{\left(t\right)}\right)^{2} + \left(\operatorname{im}{\left(t\right)}\right)^{2}} 
x1 = i*(-1.04221197690107e-51*(-7.37853735174449e+50*re(t) - 2.2635212754204e+51*im(t) + 2.71239880701756e+137)*im(t)/(re(t)^2 + im(t)^2) + 1.04221197690107e-51*(2.2635212754204e+51*re(t) - 7.37853735174449e+50*im(t) + 3.09034320354466e+136)*re(t)/(re(t)^2 + im(t)^2)) + 1.04221197690107e-51*(-7.37853735174449e+50*re(t) - 2.2635212754204e+51*im(t) + 2.71239880701756e+137)*re(t)/(re(t)^2 + im(t)^2) + 1.04221197690107e-51*(2.2635212754204e+51*re(t) - 7.37853735174449e+50*im(t) + 3.09034320354466e+136)*im(t)/(re(t)^2 + im(t)^2)
Suma y producto de raíces [src] 
suma
  /1.04221197690107e-51*(3.09034320354466e+136 + 2.2635212754204e+51*re(t) - 7.37853735174449e+50*im(t))*re(t)   1.04221197690107e-51*(2.71239880701756e+137 - 2.2635212754204e+51*im(t) - 7.37853735174449e+50*re(t))*im(t)\   1.04221197690107e-51*(2.71239880701756e+137 - 2.2635212754204e+51*im(t) - 7.37853735174449e+50*re(t))*re(t)   1.04221197690107e-51*(3.09034320354466e+136 + 2.2635212754204e+51*re(t) - 7.37853735174449e+50*im(t))*im(t)
I*|----------------------------------------------------------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------| + ----------------------------------------------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------------
  |                                                2        2                                                                                                    2        2                                                 |                                                   2        2                                                                                                    2        2                                                 
  \                                              im (t) + re (t)                                                                                               im (t) + re (t)                                              /                                                 im (t) + re (t)                                                                                               im (t) + re (t)
i(−1.04221197690107⋅10−51(−7.37853735174449⋅1050re⁡(t)−2.2635212754204⋅1051im⁡(t)+2.71239880701756⋅10137)im⁡(t)(re⁡(t))2+(im⁡(t))2+1.04221197690107⋅10−51(2.2635212754204⋅1051re⁡(t)−7.37853735174449⋅1050im⁡(t)+3.09034320354466⋅10136)re⁡(t)(re⁡(t))2+(im⁡(t))2)+1.04221197690107⋅10−51(−7.37853735174449⋅1050re⁡(t)−2.2635212754204⋅1051im⁡(t)+2.71239880701756⋅10137)re⁡(t)(re⁡(t))2+(im⁡(t))2+1.04221197690107⋅10−51(2.2635212754204⋅1051re⁡(t)−7.37853735174449⋅1050im⁡(t)+3.09034320354466⋅10136)im⁡(t)(re⁡(t))2+(im⁡(t))2i \left(- \frac{1.04221197690107 \cdot 10^{-51} \left(- 7.37853735174449 \cdot 10^{50} \operatorname{re}{\left(t\right)} - 2.2635212754204 \cdot 10^{51} \operatorname{im}{\left(t\right)} + 2.71239880701756 \cdot 10^{137}\right) \operatorname{im}{\left(t\right)}}{\left(\operatorname{re}{\left(t\right)}\right)^{2} + \left(\operatorname{im}{\left(t\right)}\right)^{2}} + \frac{1.04221197690107 \cdot 10^{-51} \left(2.2635212754204 \cdot 10^{51} \operatorname{re}{\left(t\right)} - 7.37853735174449 \cdot 10^{50} \operatorname{im}{\left(t\right)} + 3.09034320354466 \cdot 10^{136}\right) \operatorname{re}{\left(t\right)}}{\left(\operatorname{re}{\left(t\right)}\right)^{2} + \left(\operatorname{im}{\left(t\right)}\right)^{2}}\right) + \frac{1.04221197690107 \cdot 10^{-51} \left(- 7.37853735174449 \cdot 10^{50} \operatorname{re}{\left(t\right)} - 2.2635212754204 \cdot 10^{51} \operatorname{im}{\left(t\right)} + 2.71239880701756 \cdot 10^{137}\right) \operatorname{re}{\left(t\right)}}{\left(\operatorname{re}{\left(t\right)}\right)^{2} + \left(\operatorname{im}{\left(t\right)}\right)^{2}} + \frac{1.04221197690107 \cdot 10^{-51} \left(2.2635212754204 \cdot 10^{51} \operatorname{re}{\left(t\right)} - 7.37853735174449 \cdot 10^{50} \operatorname{im}{\left(t\right)} + 3.09034320354466 \cdot 10^{136}\right) \operatorname{im}{\left(t\right)}}{\left(\operatorname{re}{\left(t\right)}\right)^{2} + \left(\operatorname{im}{\left(t\right)}\right)^{2}} 
=
  /1.04221197690107e-51*(3.09034320354466e+136 + 2.2635212754204e+51*re(t) - 7.37853735174449e+50*im(t))*re(t)   1.04221197690107e-51*(2.71239880701756e+137 - 2.2635212754204e+51*im(t) - 7.37853735174449e+50*re(t))*im(t)\   1.04221197690107e-51*(2.71239880701756e+137 - 2.2635212754204e+51*im(t) - 7.37853735174449e+50*re(t))*re(t)   1.04221197690107e-51*(3.09034320354466e+136 + 2.2635212754204e+51*re(t) - 7.37853735174449e+50*im(t))*im(t)
I*|----------------------------------------------------------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------| + ----------------------------------------------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------------
  |                                                2        2                                                                                                    2        2                                                 |                                                   2        2                                                                                                    2        2                                                 
  \                                              im (t) + re (t)                                                                                               im (t) + re (t)                                              /                                                 im (t) + re (t)                                                                                               im (t) + re (t)
i(−1.04221197690107⋅10−51(−7.37853735174449⋅1050re⁡(t)−2.2635212754204⋅1051im⁡(t)+2.71239880701756⋅10137)im⁡(t)(re⁡(t))2+(im⁡(t))2+1.04221197690107⋅10−51(2.2635212754204⋅1051re⁡(t)−7.37853735174449⋅1050im⁡(t)+3.09034320354466⋅10136)re⁡(t)(re⁡(t))2+(im⁡(t))2)+1.04221197690107⋅10−51(−7.37853735174449⋅1050re⁡(t)−2.2635212754204⋅1051im⁡(t)+2.71239880701756⋅10137)re⁡(t)(re⁡(t))2+(im⁡(t))2+1.04221197690107⋅10−51(2.2635212754204⋅1051re⁡(t)−7.37853735174449⋅1050im⁡(t)+3.09034320354466⋅10136)im⁡(t)(re⁡(t))2+(im⁡(t))2i \left(- \frac{1.04221197690107 \cdot 10^{-51} \left(- 7.37853735174449 \cdot 10^{50} \operatorname{re}{\left(t\right)} - 2.2635212754204 \cdot 10^{51} \operatorname{im}{\left(t\right)} + 2.71239880701756 \cdot 10^{137}\right) \operatorname{im}{\left(t\right)}}{\left(\operatorname{re}{\left(t\right)}\right)^{2} + \left(\operatorname{im}{\left(t\right)}\right)^{2}} + \frac{1.04221197690107 \cdot 10^{-51} \left(2.2635212754204 \cdot 10^{51} \operatorname{re}{\left(t\right)} - 7.37853735174449 \cdot 10^{50} \operatorname{im}{\left(t\right)} + 3.09034320354466 \cdot 10^{136}\right) \operatorname{re}{\left(t\right)}}{\left(\operatorname{re}{\left(t\right)}\right)^{2} + \left(\operatorname{im}{\left(t\right)}\right)^{2}}\right) + \frac{1.04221197690107 \cdot 10^{-51} \left(- 7.37853735174449 \cdot 10^{50} \operatorname{re}{\left(t\right)} - 2.2635212754204 \cdot 10^{51} \operatorname{im}{\left(t\right)} + 2.71239880701756 \cdot 10^{137}\right) \operatorname{re}{\left(t\right)}}{\left(\operatorname{re}{\left(t\right)}\right)^{2} + \left(\operatorname{im}{\left(t\right)}\right)^{2}} + \frac{1.04221197690107 \cdot 10^{-51} \left(2.2635212754204 \cdot 10^{51} \operatorname{re}{\left(t\right)} - 7.37853735174449 \cdot 10^{50} \operatorname{im}{\left(t\right)} + 3.09034320354466 \cdot 10^{136}\right) \operatorname{im}{\left(t\right)}}{\left(\operatorname{re}{\left(t\right)}\right)^{2} + \left(\operatorname{im}{\left(t\right)}\right)^{2}} 
producto
  /1.04221197690107e-51*(3.09034320354466e+136 + 2.2635212754204e+51*re(t) - 7.37853735174449e+50*im(t))*re(t)   1.04221197690107e-51*(2.71239880701756e+137 - 2.2635212754204e+51*im(t) - 7.37853735174449e+50*re(t))*im(t)\   1.04221197690107e-51*(2.71239880701756e+137 - 2.2635212754204e+51*im(t) - 7.37853735174449e+50*re(t))*re(t)   1.04221197690107e-51*(3.09034320354466e+136 + 2.2635212754204e+51*re(t) - 7.37853735174449e+50*im(t))*im(t)
I*|----------------------------------------------------------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------| + ----------------------------------------------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------------
  |                                                2        2                                                                                                    2        2                                                 |                                                   2        2                                                                                                    2        2                                                 
  \                                              im (t) + re (t)                                                                                               im (t) + re (t)                                              /                                                 im (t) + re (t)                                                                                               im (t) + re (t)
i(−1.04221197690107⋅10−51(−7.37853735174449⋅1050re⁡(t)−2.2635212754204⋅1051im⁡(t)+2.71239880701756⋅10137)im⁡(t)(re⁡(t))2+(im⁡(t))2+1.04221197690107⋅10−51(2.2635212754204⋅1051re⁡(t)−7.37853735174449⋅1050im⁡(t)+3.09034320354466⋅10136)re⁡(t)(re⁡(t))2+(im⁡(t))2)+1.04221197690107⋅10−51(−7.37853735174449⋅1050re⁡(t)−2.2635212754204⋅1051im⁡(t)+2.71239880701756⋅10137)re⁡(t)(re⁡(t))2+(im⁡(t))2+1.04221197690107⋅10−51(2.2635212754204⋅1051re⁡(t)−7.37853735174449⋅1050im⁡(t)+3.09034320354466⋅10136)im⁡(t)(re⁡(t))2+(im⁡(t))2i \left(- \frac{1.04221197690107 \cdot 10^{-51} \left(- 7.37853735174449 \cdot 10^{50} \operatorname{re}{\left(t\right)} - 2.2635212754204 \cdot 10^{51} \operatorname{im}{\left(t\right)} + 2.71239880701756 \cdot 10^{137}\right) \operatorname{im}{\left(t\right)}}{\left(\operatorname{re}{\left(t\right)}\right)^{2} + \left(\operatorname{im}{\left(t\right)}\right)^{2}} + \frac{1.04221197690107 \cdot 10^{-51} \left(2.2635212754204 \cdot 10^{51} \operatorname{re}{\left(t\right)} - 7.37853735174449 \cdot 10^{50} \operatorname{im}{\left(t\right)} + 3.09034320354466 \cdot 10^{136}\right) \operatorname{re}{\left(t\right)}}{\left(\operatorname{re}{\left(t\right)}\right)^{2} + \left(\operatorname{im}{\left(t\right)}\right)^{2}}\right) + \frac{1.04221197690107 \cdot 10^{-51} \left(- 7.37853735174449 \cdot 10^{50} \operatorname{re}{\left(t\right)} - 2.2635212754204 \cdot 10^{51} \operatorname{im}{\left(t\right)} + 2.71239880701756 \cdot 10^{137}\right) \operatorname{re}{\left(t\right)}}{\left(\operatorname{re}{\left(t\right)}\right)^{2} + \left(\operatorname{im}{\left(t\right)}\right)^{2}} + \frac{1.04221197690107 \cdot 10^{-51} \left(2.2635212754204 \cdot 10^{51} \operatorname{re}{\left(t\right)} - 7.37853735174449 \cdot 10^{50} \operatorname{im}{\left(t\right)} + 3.09034320354466 \cdot 10^{136}\right) \operatorname{im}{\left(t\right)}}{\left(\operatorname{re}{\left(t\right)}\right)^{2} + \left(\operatorname{im}{\left(t\right)}\right)^{2}} 
=
    /                                                                  2              2                                                          2                           2                                  \
1.0*\3.22079269946906e+85*im(t) + 2.82689452280588e+86*re(t) - 0.769*im (t) - 0.769*re (t) + 3.22079269946906e+85*I*re(t) + 2.35906898321353*I*im (t) + 2.35906898321353*I*re (t) - 2.82689452280588e+86*I*im(t)/
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                   2        2                                                                                                    
                                                                                                 im (t) + re (t)
1.0(−0.769(re⁡(t))2+2.35906898321353i(re⁡(t))2+2.82689452280588⋅1086re⁡(t)+3.22079269946906⋅1085ire⁡(t)−0.769(im⁡(t))2+2.35906898321353i(im⁡(t))2+3.22079269946906⋅1085im⁡(t)−2.82689452280588⋅1086iim⁡(t))(re⁡(t))2+(im⁡(t))2\frac{1.0 \left(- 0.769 \left(\operatorname{re}{\left(t\right)}\right)^{2} + 2.35906898321353 i \left(\operatorname{re}{\left(t\right)}\right)^{2} + 2.82689452280588 \cdot 10^{86} \operatorname{re}{\left(t\right)} + 3.22079269946906 \cdot 10^{85} i \operatorname{re}{\left(t\right)} - 0.769 \left(\operatorname{im}{\left(t\right)}\right)^{2} + 2.35906898321353 i \left(\operatorname{im}{\left(t\right)}\right)^{2} + 3.22079269946906 \cdot 10^{85} \operatorname{im}{\left(t\right)} - 2.82689452280588 \cdot 10^{86} i \operatorname{im}{\left(t\right)}\right)}{\left(\operatorname{re}{\left(t\right)}\right)^{2} + \left(\operatorname{im}{\left(t\right)}\right)^{2}} 
1.0*(3.22079269946906e+85*im(t) + 2.82689452280588e+86*re(t) - 0.769*im(t)^2 - 0.769*re(t)^2 + 3.22079269946906e+85*i*re(t) + 2.35906898321353*i*im(t)^2 + 2.35906898321353*i*re(t)^2 - 2.82689452280588e+86*i*im(t))/(im(t)^2 + re(t)^2)
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