作者CRAZYAWIND (怒火烧不尽)
看板Grad-ProbAsk
标题Re: [理工] [工数]-一阶O.D.E
时间Tue Oct 6 13:41:21 2009
※ 引述《nicksean (阿祥)》之铭言：
: y'=3(y+2x)+1, y(0)=0
: ans:y(x)=e^3x-2x-1
: 我积分指数函数时候积不太出来,
: 麻烦各位帮帮我解这一题
: 谢谢
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
在来个快一点的逆运算子
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
--
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◆ From: 59.105.159.190
1F：→ iyenn:待定系数不是更快...长除都不用.....=.= 10/06 13:52
2F：推 mdpming:感觉积分因子比较快也QQ 10/06 16:06
3F：→ CRAZYAWIND:反正都很快啦= = 一题不用3分钟的= = 10/06 16:54
4F：推 nicksean:感恩!我刚刚也才想出来怎麽解...谢谢各位 10/07 02:50