Sr Examen
Ecuación diferencial y''+6y'+13y=sint+sin2t+4tcos2t
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
2
d d
6*--(y(t)) + 13*y(t) + ---(y(t)) = 4*t*cos(2*t) + sin(t) + sin(2*t)
dt 2
dt
$$13 y{\left(t \right)} + 6 \frac{d}{d t} y{\left(t \right)} + \frac{d^{2}}{d t^{2}} y{\left(t \right)} = 4 t \cos{\left(2 t \right)} + \sin{\left(t \right)} + \sin{\left(2 t \right)}$$
13*y + 6*y' + y'' = 4*t*cos(2*t) + sin(t) + sin(2*t)
Respuesta
[src]
463*sin(2*t) 172*cos(2*t) cos(t) sin(t) -3*t 4*t*cos(2*t) 16*t*sin(2*t)
y(t) = - ------------ - ------------ - ------ + ------ + (C1*sin(2*t) + C2*cos(2*t))*e + ------------ + -------------
5625 1875 30 15 25 75
$$y{\left(t \right)} = \frac{16 t \sin{\left(2 t \right)}}{75} + \frac{4 t \cos{\left(2 t \right)}}{25} + \left(C_{1} \sin{\left(2 t \right)} + C_{2} \cos{\left(2 t \right)}\right) e^{- 3 t} + \frac{\sin{\left(t \right)}}{15} - \frac{463 \sin{\left(2 t \right)}}{5625} - \frac{\cos{\left(t \right)}}{30} - \frac{172 \cos{\left(2 t \right)}}{1875}$$
Clasificación
nth linear constant coeff undetermined coefficients
nth linear constant coeff variation of parameters
nth linear constant coeff variation of parameters Integral