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((4*y*d^3)/(d*t^3))+((5*y*d^2)/(d*t^2))+((6*d*y)/(d*t))+y=(d*u)/(d*t)+u la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
     3        2                      
4*y*d    5*y*d    6*d*y       d*u    
------ + ------ + ----- + y = --- + u
    3        2     d*t        d*t    
 d*t      d*t
$$y + \left(\left(\frac{d^{3} \cdot 4 y}{d t^{3}} + \frac{d^{2} \cdot 5 y}{d t^{2}}\right) + \frac{6 d y}{d t}\right) = u + \frac{d u}{d t}$$
Simplificar
Gráfica
Respuesta rápida [src] 
       /              /             2          \           /             2          \\                 /             2          \           /             2          \
       |              |          u*t           |           |          u*t           ||                 |          u*t           |           |          u*t           |
y1 = I*|(1 + re(t))*im|------------------------| + im(t)*re|------------------------|| + (1 + re(t))*re|------------------------| - im(t)*im|------------------------|
       |              | 3      2      2        |           | 3      2      2        ||                 | 3      2      2        |           | 3      2      2        |
       \              \t  + 4*d  + 6*t  + 5*d*t/           \t  + 4*d  + 6*t  + 5*d*t//                 \t  + 4*d  + 6*t  + 5*d*t/           \t  + 4*d  + 6*t  + 5*d*t/
$$y_{1} = i \left(\left(\operatorname{re}{\left(t\right)} + 1\right) \operatorname{im}{\left(\frac{t^{2} u}{4 d^{2} + 5 d t + t^{3} + 6 t^{2}}\right)} + \operatorname{re}{\left(\frac{t^{2} u}{4 d^{2} + 5 d t + t^{3} + 6 t^{2}}\right)} \operatorname{im}{\left(t\right)}\right) + \left(\operatorname{re}{\left(t\right)} + 1\right) \operatorname{re}{\left(\frac{t^{2} u}{4 d^{2} + 5 d t + t^{3} + 6 t^{2}}\right)} - \operatorname{im}{\left(t\right)} \operatorname{im}{\left(\frac{t^{2} u}{4 d^{2} + 5 d t + t^{3} + 6 t^{2}}\right)}$$ 
y1 = i*((re(t) + 1)*im(t^2*u/(4*d^2 + 5*d*t + t^3 + 6*t^2)) + re(t^2*u/(4*d^2 + 5*d*t + t^3 + 6*t^2))*im(t)) + (re(t) + 1)*re(t^2*u/(4*d^2 + 5*d*t + t^3 + 6*t^2)) - im(t)*im(t^2*u/(4*d^2 + 5*d*t + t^3 + 6*t^2))
Suma y producto de raíces [src] 
suma
  /              /             2          \           /             2          \\                 /             2          \           /             2          \
  |              |          u*t           |           |          u*t           ||                 |          u*t           |           |          u*t           |
I*|(1 + re(t))*im|------------------------| + im(t)*re|------------------------|| + (1 + re(t))*re|------------------------| - im(t)*im|------------------------|
  |              | 3      2      2        |           | 3      2      2        ||                 | 3      2      2        |           | 3      2      2        |
  \              \t  + 4*d  + 6*t  + 5*d*t/           \t  + 4*d  + 6*t  + 5*d*t//                 \t  + 4*d  + 6*t  + 5*d*t/           \t  + 4*d  + 6*t  + 5*d*t/
$$i \left(\left(\operatorname{re}{\left(t\right)} + 1\right) \operatorname{im}{\left(\frac{t^{2} u}{4 d^{2} + 5 d t + t^{3} + 6 t^{2}}\right)} + \operatorname{re}{\left(\frac{t^{2} u}{4 d^{2} + 5 d t + t^{3} + 6 t^{2}}\right)} \operatorname{im}{\left(t\right)}\right) + \left(\operatorname{re}{\left(t\right)} + 1\right) \operatorname{re}{\left(\frac{t^{2} u}{4 d^{2} + 5 d t + t^{3} + 6 t^{2}}\right)} - \operatorname{im}{\left(t\right)} \operatorname{im}{\left(\frac{t^{2} u}{4 d^{2} + 5 d t + t^{3} + 6 t^{2}}\right)}$$ 
=
  /              /             2          \           /             2          \\                 /             2          \           /             2          \
  |              |          u*t           |           |          u*t           ||                 |          u*t           |           |          u*t           |
I*|(1 + re(t))*im|------------------------| + im(t)*re|------------------------|| + (1 + re(t))*re|------------------------| - im(t)*im|------------------------|
  |              | 3      2      2        |           | 3      2      2        ||                 | 3      2      2        |           | 3      2      2        |
  \              \t  + 4*d  + 6*t  + 5*d*t/           \t  + 4*d  + 6*t  + 5*d*t//                 \t  + 4*d  + 6*t  + 5*d*t/           \t  + 4*d  + 6*t  + 5*d*t/
$$i \left(\left(\operatorname{re}{\left(t\right)} + 1\right) \operatorname{im}{\left(\frac{t^{2} u}{4 d^{2} + 5 d t + t^{3} + 6 t^{2}}\right)} + \operatorname{re}{\left(\frac{t^{2} u}{4 d^{2} + 5 d t + t^{3} + 6 t^{2}}\right)} \operatorname{im}{\left(t\right)}\right) + \left(\operatorname{re}{\left(t\right)} + 1\right) \operatorname{re}{\left(\frac{t^{2} u}{4 d^{2} + 5 d t + t^{3} + 6 t^{2}}\right)} - \operatorname{im}{\left(t\right)} \operatorname{im}{\left(\frac{t^{2} u}{4 d^{2} + 5 d t + t^{3} + 6 t^{2}}\right)}$$ 
producto
  /              /             2          \           /             2          \\                 /             2          \           /             2          \
  |              |          u*t           |           |          u*t           ||                 |          u*t           |           |          u*t           |
I*|(1 + re(t))*im|------------------------| + im(t)*re|------------------------|| + (1 + re(t))*re|------------------------| - im(t)*im|------------------------|
  |              | 3      2      2        |           | 3      2      2        ||                 | 3      2      2        |           | 3      2      2        |
  \              \t  + 4*d  + 6*t  + 5*d*t/           \t  + 4*d  + 6*t  + 5*d*t//                 \t  + 4*d  + 6*t  + 5*d*t/           \t  + 4*d  + 6*t  + 5*d*t/
$$i \left(\left(\operatorname{re}{\left(t\right)} + 1\right) \operatorname{im}{\left(\frac{t^{2} u}{4 d^{2} + 5 d t + t^{3} + 6 t^{2}}\right)} + \operatorname{re}{\left(\frac{t^{2} u}{4 d^{2} + 5 d t + t^{3} + 6 t^{2}}\right)} \operatorname{im}{\left(t\right)}\right) + \left(\operatorname{re}{\left(t\right)} + 1\right) \operatorname{re}{\left(\frac{t^{2} u}{4 d^{2} + 5 d t + t^{3} + 6 t^{2}}\right)} - \operatorname{im}{\left(t\right)} \operatorname{im}{\left(\frac{t^{2} u}{4 d^{2} + 5 d t + t^{3} + 6 t^{2}}\right)}$$ 
=
  /              /             2          \           /             2          \\                 /             2          \           /             2          \
  |              |          u*t           |           |          u*t           ||                 |          u*t           |           |          u*t           |
I*|(1 + re(t))*im|------------------------| + im(t)*re|------------------------|| + (1 + re(t))*re|------------------------| - im(t)*im|------------------------|
  |              | 3      2      2        |           | 3      2      2        ||                 | 3      2      2        |           | 3      2      2        |
  \              \t  + 4*d  + 6*t  + 5*d*t/           \t  + 4*d  + 6*t  + 5*d*t//                 \t  + 4*d  + 6*t  + 5*d*t/           \t  + 4*d  + 6*t  + 5*d*t/
$$i \left(\left(\operatorname{re}{\left(t\right)} + 1\right) \operatorname{im}{\left(\frac{t^{2} u}{4 d^{2} + 5 d t + t^{3} + 6 t^{2}}\right)} + \operatorname{re}{\left(\frac{t^{2} u}{4 d^{2} + 5 d t + t^{3} + 6 t^{2}}\right)} \operatorname{im}{\left(t\right)}\right) + \left(\operatorname{re}{\left(t\right)} + 1\right) \operatorname{re}{\left(\frac{t^{2} u}{4 d^{2} + 5 d t + t^{3} + 6 t^{2}}\right)} - \operatorname{im}{\left(t\right)} \operatorname{im}{\left(\frac{t^{2} u}{4 d^{2} + 5 d t + t^{3} + 6 t^{2}}\right)}$$ 
i*((1 + re(t))*im(u*t^2/(t^3 + 4*d^2 + 6*t^2 + 5*d*t)) + im(t)*re(u*t^2/(t^3 + 4*d^2 + 6*t^2 + 5*d*t))) + (1 + re(t))*re(u*t^2/(t^3 + 4*d^2 + 6*t^2 + 5*d*t)) - im(t)*im(u*t^2/(t^3 + 4*d^2 + 6*t^2 + 5*d*t))
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