Sr Examen
Ecuación diferencial y""'+4y"'=2+te^(2t)+sin(2t)
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Solución
Ha introducido
[src]
3 5
d d 2*t
4*---(y(t)) + ---(y(t)) = 2 + t*e + sin(2*t)
3 5
dt dt
$$4 \frac{d^{3}}{d t^{3}} y{\left(t \right)} + \frac{d^{5}}{d t^{5}} y{\left(t \right)} = t e^{2 t} + \sin{\left(2 t \right)} + 2$$
4*y''' + y''''' = t*exp(2*t) + sin(2*t) + 2
Respuesta
[src]
2*t 3 / 2*t\
e t 2 | sin(2*t) e |
y(t) = C1 - ---- + -- + C2*t + C4*sin(2*t) + C5*cos(2*t) + t*|C3 + -------- + ----|
32 12 \ 32 64 /
$$y{\left(t \right)} = C_{1} + C_{2} t^{2} + C_{4} \sin{\left(2 t \right)} + C_{5} \cos{\left(2 t \right)} + \frac{t^{3}}{12} + t \left(C_{3} + \frac{e^{2 t}}{64} + \frac{\sin{\left(2 t \right)}}{32}\right) - \frac{e^{2 t}}{32}$$
Clasificación
nth linear constant coeff undetermined coefficients
nth linear constant coeff variation of parameters
nth order reducible
nth linear constant coeff variation of parameters Integral