作者topee (eason)
看板Grad-ProbAsk
標題 [理工] [工數]-簡單ODE ~"~
時間Mon Apr 12 23:07:16 2010
dy 1
---= ------
dx x+y+1
(x+y+1)dy-dx=0
令u=x+y . y =u-x . dy=du-dx
x(du-dx)+(u-x)(du-dx)+(du-dx)-dx=0
u(du-dx)+du-2dx = 0
(u+1)du-(u+2)dx=0
(u+1)
-----du -dx = 0
(u+2)
1
---ln(u+2)^2 + ln(u+2) -x = c
2
1
---ln(x+y+2)^2 + ln(x+y+2) -x = c
2
這樣算對嗎?
u
----du 積分 有人能白話解釋 一下積分嗎?
u+2
我怕我觀念錯了..
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◆ From: 125.228.217.251
→ funtsung:[(u+2)-2]/(u+2) = 1 - 2/u+2 ==> u-2ln(u+2) 04/12 23:09
→ iyenn:分子分母幕次相同,先化簡 04/12 23:10
→ topee:? 我都做錯? 04/12 23:12
推 ntust661:錯 04/12 23:16
推 squallting:一題15分 我給3分 04/12 23:19
→ topee:不能分開積分 ? 04/12 23:41
推 mdpming:T大還沒考完喔@@ 04/13 00:08
→ topee:學海無崖.... 04/13 00:34