Re: [理工] [工數]-一階O.D.E
※ 引述《nicksean (阿祥)》之銘言：
: y'=3(y+2x)+1, y(0)=0
: ans:y(x)=e^3x-2x-1
: 我積分指數函數時候積不太出來,
: 麻煩各位幫幫我解這一題
: 謝謝
y' - 3y = 6x +1
S -3 dx -3x
I(x) = e = e
-3x -3x -3x
Iy = S e (6x+1) dx = (-2x - 1/3)e - 2/3 e + c1
-3x
= (-2x - 1) e + c1
3x
y = (-2x -1 ) + c1e
代入 IC -1 + C1 =0 C1=1
3x
y = e -2x -1
by part
-3x
6x+1 e
-3x
-6 -1/3 e
-3x
0 1/9 e
在來個快一點的逆運算子
y' - 3y = 6x+1
mx
令y = e
m - 3 = 0 m = 3
3x
yh = c1e
1
yp = ──── 6x+1
D - 3
= (-1/3 - D/9) (6x+1)
= -2x -1
3x
y = yh + yp = c1e -2x -1
3x
代入IC 可得 y = e -2x -1
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 59.105.159.190
→
10/06 13:52, , 1F
10/06 13:52, 1F
推
10/06 16:06, , 2F
10/06 16:06, 2F
→
10/06 16:54, , 3F
10/06 16:54, 3F
推
10/07 02:50, , 4F
10/07 02:50, 4F
討論串 (同標題文章)
本文引述了以下文章的的內容：
完整討論串 (本文為第 6 之 9 篇)：