[理工] [工數]-聯立ODE
限定使用消去法
x'=-2x+y -----{1}
{
y'=-4x+3y+10 cos t-----{2}
y=x'+2x , y'=x''+2x'接代入{2}
得x''-x'-2x=10 cost
-t 2t t
x =c1e +c2e , W=3e
h
let x =u1x1+u2x2
p
t -2t
得u1=(-3/7)e (cos t+sin t) u2=(3/22)e (sint-2cost)
這裡就發現根答案不一樣了
-t 2t
答案為 x(t)=c1e +c2e -3cos t-sin t
是哪個環節出錯嗎= =? 請指教!!
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 218.166.13.235
推
01/31 00:17, , 1F
01/31 00:17, 1F
→
01/31 00:21, , 2F
01/31 00:21, 2F
→
01/31 00:24, , 3F
01/31 00:24, 3F
→
01/31 00:26, , 4F
01/31 00:26, 4F
→
01/31 00:29, , 5F
01/31 00:29, 5F
→
01/31 00:32, , 6F
01/31 00:32, 6F
→
01/31 00:34, , 7F
01/31 00:34, 7F
→
01/31 00:35, , 8F
01/31 00:35, 8F
→
01/31 00:35, , 9F
01/31 00:35, 9F
→
01/31 00:36, , 10F
01/31 00:36, 10F
→
01/31 00:36, , 11F
01/31 00:36, 11F
→
01/31 00:36, , 12F
01/31 00:36, 12F
→
01/31 00:37, , 13F
01/31 00:37, 13F
看到了= =..有打錯..3Q.b大
※ 編輯: smallprawn 來自: 218.166.13.235 (01/31 00:38)
→
01/31 00:38, , 14F
01/31 00:38, 14F
→
01/31 00:41, , 15F
01/31 00:41, 15F
推
01/31 00:57, , 16F
01/31 00:57, 16F
→
01/31 00:58, , 17F
01/31 00:58, 17F
→
01/31 01:01, , 18F
01/31 01:01, 18F
以u1來說..我解成這樣..哪裡錯了= =...
u1=∫- (e^2t)(10cost)/(3e^t)
D I
e^t cost
e^t sint
e^t -cost -10/3∫e^t cost dt=e^t(sint+cost)-∫e^t cost dt
(-10/3 +1)∫e^t cost dt=e^t(sint+cost)
∫e^t cost dt=(-3/7)e^t(sint+cost)
※ 編輯: smallprawn 來自: 218.166.13.235 (01/31 01:07)
推
01/31 01:11, , 19F
01/31 01:11, 19F
→
01/31 01:11, , 20F
01/31 01:11, 20F
→
01/31 01:12, , 21F
01/31 01:12, 21F
→
01/31 01:42, , 22F
01/31 01:42, 22F
討論串 (同標題文章)