作者CRAZYAWIND (怒火燒不盡)
看板Grad-ProbAsk
標題Re: [理工] [工數]-一階O.D.E
時間Tue Oct 6 13:41:21 2009
※ 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
1F：→ iyenn:待定係數不是更快...長除都不用.....=.= 10/06 13:52
2F：推 mdpming:感覺積分因子比較快也QQ 10/06 16:06
3F：→ CRAZYAWIND:反正都很快啦= = 一題不用3分鐘的= = 10/06 16:54
4F：推 nicksean:感恩!我剛剛也才想出來怎麼解...謝謝各位 10/07 02:50