作者iyenn (曉風)
看板Grad-ProbAsk
標題Re: [理工] [工數]-高階ODE Euler cauchy方程
時間Thu Dec 10 00:15:15 2009
※ 引述《CRAZYAWIND (怒火燒不盡)》之銘言：
: 3 2 6x^3
: x y''' - 4x y'' + 8xy' - 8y = ──────── <<94中興化工>>
: (x^2 + 1 )^3/2
: 這題yp項= = 我算了好久 用部份分式 或是重積分法 加上 三角代換
: 都展不回他給的答案 3 5
: 2 4 2x + 4x + 2x
: y(x) = c1x + c2x + c3x - ─────────
: √(1+x^2)
3 2 6x^3
x y''' - 4x y'' + 8xy' - 8y = ────────
(x^2 + 1 )^3/2
x=e^t lnx=t D=d/dt
(D(D-1)(D-2)-4D(D-1)+8D-8)y=6e^3t/(e^2t+1)^3/2
(D(D^2-3D+2-4D+4)+8(D-1))y=...
(D(D-6)(D-1)+8(D-1))y=...
((D-1)(D-2)(D-4))y=...
1 6e^3t
y=--------------- -------------------
(D-1)(D-2)(D-4) (e^2t+1)^3/2
1 2e^3t
yp1=----- --------------------
D-1 (e^2t+1)^3/2
=e^t∫2e^2t(e^2t+1)^-3/2dt
=-2e^t(e^2t+1)^-1/2
-2x
=-----------
(x^2+1)^1/2
1 -3e^3t
yp2=----- -----------------
D-2 (e^2t+1)^3/2
=e^2t∫-3e^t(e^2t+1)^-3/2dt
=x^2∫-3(x^2+1)^-3/2dx
-3x
=x^2----------
(x^2+1)^1/2
1 e^3t
yp3=----- -----------------
D-4 (e^2t+1)^3/2
e^-t
=e^4t∫------------dt
(e^2t+1)^3/2
1
=x^4∫--------------dx
x^2(x^2+1)^3/2
----------------------------------------------------------------
1 1 1
∫--------------dx=------------ +2∫--------------dx
x^2(x^2+1)^3/2 x(x^2+1)^1/2 x^2(x^2+1)^1/2
->分部 and let x=tan?....#$%@#&$#!!@@
-(x^2+1)^1/2
=............. +2------------
x
1 -(2x^2+2)
=------------ + ------------
x(x^2+1)^1/2 x(x^2+1)^1/2
----------------------------------------------------------
-x^3-2x^5
=--------------
(x^2+1)^1/2
yp=yp1+2+3 (茶~)
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◆ From: 123.193.214.165
1F：→ iyenn:打錯就算了....愛睏 12/10 00:16
2F：→ iyenn:好像不用分也可以(逃 12/10 00:25
3F：推 CRAZYAWIND:i大你就安心的去睡覺吧= = 12/10 00:27
4F：推 shinyhaung:我突然覺得我浪費一年重考... 12/10 00:29
5F：→ iyenn:s大也考電信嗎@_@y~ 12/10 00:56
6F：推 CRAZYAWIND:前兩個跟我做的一樣= = 第三個D-4 那項的BY PART 12/10 01:14
7F：→ CRAZYAWIND:看的很混亂= = 12/10 01:14