→ mdpming:原來是取實部..qq 07/27 22:32
推 xylooki:如果用變係數的方法做呢? 答案好像不一樣 ! 07/27 22:54
→ iyenn:3階的變係數 怎麼令的教一下XD 07/27 23:45
→ iyenn:耍笨了= = 證了一下 令法一樣XD 07/27 23:57
d
let x=e^t lnx=t D=---
dt
D(D-1)(D-2)y+2Dy-2y=te^2t + 3e^t
(D^3-3D^2+4D-2)y=....
(D-1)(D^2-2D+2)yh=0
yh=c1e^t + e^t(Acos(t)+Bsin(t))
1
yp1=---------------te^2t
(D-1)(D^2-2D+2)
1
=e^2t---------------t
(D+1)(D^2+2D+2)
=e^2t( 0.5 - D +....)t
=(0.5t-1)e^2t
1
yp2=--------------- 3e^t
(D-1)(D^2-2D+2)
1
=e^t ------------- 3
(D)(D^2+1)
1
=e^t ------------- 3t
(D^2+1)
=e^t (3t)
y=c1e^t + e^t(Acos(t)+Bsin(t)) +(0.5t-1)e^2t +e^t (3t)
=c1x +x(Acos(lnx)+Bsin(lnx)) + (0.5lnx -1)x^2 +x(3lnx)
--
為者常成.行者常至
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 123.193.214.165
※ 編輯: iyenn 來自: 123.193.214.165 (07/27 21:35)