Sr Examen
Ecuación diferencial y'''-4*y''-(y')+4*y=3*e^(-t)
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
2 3
d d d -t
- --(y(t)) - 4*---(y(t)) + 4*y(t) + ---(y(t)) = 3*e
dt 2 3
dt dt
$$4 y{\left(t \right)} - \frac{d}{d t} y{\left(t \right)} - 4 \frac{d^{2}}{d t^{2}} y{\left(t \right)} + \frac{d^{3}}{d t^{3}} y{\left(t \right)} = 3 e^{- t}$$
4*y - y' - 4*y'' + y''' = 3*exp(-t)
Respuesta
[src]
t 4*t / 3*t\ -t
y(t) = C2*e + C3*e + |C1 + ---|*e
\ 10/
$$y{\left(t \right)} = C_{2} e^{t} + C_{3} e^{4 t} + \left(C_{1} + \frac{3 t}{10}\right) e^{- t}$$
Clasificación
nth linear constant coeff undetermined coefficients
nth linear constant coeff variation of parameters
nth linear constant coeff variation of parameters Integral