作者youmehim (哩挖伊)
看板Grad-ProbAsk
标题Re: [理工] [工数]-一阶ODE
时间Wed Jul 22 12:36:45 2009
※ 引述《ecko1023 (NEIGHBORHOOD)》之铭言：
: dy xy^2-cosx sinx
: ---- = ------------------ y(0)=2
: dx y(1-x^2)
: 有请神人了!!
: 我这题算超久...
2
xy - cosx sinx
y'=----------------
2
y ( 1 - x )
2 2
( x y - y ) dy + ( xy - cosx sinx ) dx = 0
因d(xy) = x dy + y dx
原式可化为
1
(xy) d(xy) - y dy - --- sin2x dx = 0
2
1 2 1 2 1
---(xy) - --- y + --- cos2x = c'
2 2 4
2 2
2(xy) - 2y + cos2x = c
代入IC y(0) = 2
0 - 8 + 1 = -7 = c
2 2
2(xy) - 2y + cos2x + 7 = 0
--
※ 发信站: 批踢踢实业坊(ptt.cc)
◆ From: 58.114.170.39
※ 编辑: youmehim 来自: 58.114.170.39 (07/22 12:39)
1F：→ ecko1023:高手~感谢!! 07/22 16:17
2F：推 ecko1023:案案案案案案案案案案案 原来我昨天题目超错难怪算不出 07/22 16:27
3F：→ ecko1023:来..=.= 还是很谢谢你!! 07/22 16:28