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y=1+1/2e^(-4t)-1/2e^(-2t) la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
         -4*t    -2*t
        E       E    
y = 1 + ----- - -----
          2       2
$$y = \left(1 + \frac{e^{- 4 t}}{2}\right) - \frac{e^{- 2 t}}{2}$$
Simplificar
Gráfica
Respuesta rápida [src] 
           / -2*re(t)                 -4*re(t)             \                 -4*re(t)                 -2*re(t)
           |e        *sin(2*im(t))   e        *sin(4*im(t))|   cos(4*im(t))*e           cos(2*im(t))*e        
y1 = 1 + I*|---------------------- - ----------------------| + ---------------------- - ----------------------
           \          2                        2           /             2                        2
$$y_{1} = i \left(\frac{e^{- 2 \operatorname{re}{\left(t\right)}} \sin{\left(2 \operatorname{im}{\left(t\right)} \right)}}{2} - \frac{e^{- 4 \operatorname{re}{\left(t\right)}} \sin{\left(4 \operatorname{im}{\left(t\right)} \right)}}{2}\right) + 1 - \frac{e^{- 2 \operatorname{re}{\left(t\right)}} \cos{\left(2 \operatorname{im}{\left(t\right)} \right)}}{2} + \frac{e^{- 4 \operatorname{re}{\left(t\right)}} \cos{\left(4 \operatorname{im}{\left(t\right)} \right)}}{2}$$ 
y1 = i*(exp(-2*re(t))*sin(2*im(t))/2 - exp(-4*re(t))*sin(4*im(t))/2) + 1 - exp(-2*re(t))*cos(2*im(t))/2 + exp(-4*re(t))*cos(4*im(t))/2
Suma y producto de raíces [src] 
suma
      / -2*re(t)                 -4*re(t)             \                 -4*re(t)                 -2*re(t)
      |e        *sin(2*im(t))   e        *sin(4*im(t))|   cos(4*im(t))*e           cos(2*im(t))*e        
1 + I*|---------------------- - ----------------------| + ---------------------- - ----------------------
      \          2                        2           /             2                        2
$$i \left(\frac{e^{- 2 \operatorname{re}{\left(t\right)}} \sin{\left(2 \operatorname{im}{\left(t\right)} \right)}}{2} - \frac{e^{- 4 \operatorname{re}{\left(t\right)}} \sin{\left(4 \operatorname{im}{\left(t\right)} \right)}}{2}\right) + 1 - \frac{e^{- 2 \operatorname{re}{\left(t\right)}} \cos{\left(2 \operatorname{im}{\left(t\right)} \right)}}{2} + \frac{e^{- 4 \operatorname{re}{\left(t\right)}} \cos{\left(4 \operatorname{im}{\left(t\right)} \right)}}{2}$$ 
=
      / -2*re(t)                 -4*re(t)             \                 -4*re(t)                 -2*re(t)
      |e        *sin(2*im(t))   e        *sin(4*im(t))|   cos(4*im(t))*e           cos(2*im(t))*e        
1 + I*|---------------------- - ----------------------| + ---------------------- - ----------------------
      \          2                        2           /             2                        2
$$i \left(\frac{e^{- 2 \operatorname{re}{\left(t\right)}} \sin{\left(2 \operatorname{im}{\left(t\right)} \right)}}{2} - \frac{e^{- 4 \operatorname{re}{\left(t\right)}} \sin{\left(4 \operatorname{im}{\left(t\right)} \right)}}{2}\right) + 1 - \frac{e^{- 2 \operatorname{re}{\left(t\right)}} \cos{\left(2 \operatorname{im}{\left(t\right)} \right)}}{2} + \frac{e^{- 4 \operatorname{re}{\left(t\right)}} \cos{\left(4 \operatorname{im}{\left(t\right)} \right)}}{2}$$ 
producto
      / -2*re(t)                 -4*re(t)             \                 -4*re(t)                 -2*re(t)
      |e        *sin(2*im(t))   e        *sin(4*im(t))|   cos(4*im(t))*e           cos(2*im(t))*e        
1 + I*|---------------------- - ----------------------| + ---------------------- - ----------------------
      \          2                        2           /             2                        2
$$i \left(\frac{e^{- 2 \operatorname{re}{\left(t\right)}} \sin{\left(2 \operatorname{im}{\left(t\right)} \right)}}{2} - \frac{e^{- 4 \operatorname{re}{\left(t\right)}} \sin{\left(4 \operatorname{im}{\left(t\right)} \right)}}{2}\right) + 1 - \frac{e^{- 2 \operatorname{re}{\left(t\right)}} \cos{\left(2 \operatorname{im}{\left(t\right)} \right)}}{2} + \frac{e^{- 4 \operatorname{re}{\left(t\right)}} \cos{\left(4 \operatorname{im}{\left(t\right)} \right)}}{2}$$ 
=
/   4*re(t)     /                 2*re(t)             \                 2*re(t)               \  -4*re(t)
\2*e        + I*\-sin(4*im(t)) + e       *sin(2*im(t))/ - cos(2*im(t))*e        + cos(4*im(t))/*e        
---------------------------------------------------------------------------------------------------------
                                                    2
$$\frac{\left(i \left(e^{2 \operatorname{re}{\left(t\right)}} \sin{\left(2 \operatorname{im}{\left(t\right)} \right)} - \sin{\left(4 \operatorname{im}{\left(t\right)} \right)}\right) + 2 e^{4 \operatorname{re}{\left(t\right)}} - e^{2 \operatorname{re}{\left(t\right)}} \cos{\left(2 \operatorname{im}{\left(t\right)} \right)} + \cos{\left(4 \operatorname{im}{\left(t\right)} \right)}\right) e^{- 4 \operatorname{re}{\left(t\right)}}}{2}$$ 
(2*exp(4*re(t)) + i*(-sin(4*im(t)) + exp(2*re(t))*sin(2*im(t))) - cos(2*im(t))*exp(2*re(t)) + cos(4*im(t)))*exp(-4*re(t))/2
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