作者liltwnboiz (TCL)
看板NTU-Exam
标题[试题] 99上 王振男 微积分乙上 第六次小考详解
时间Wed Dec 15 21:09:31 2010
※ 引述《shokanshorin (上官蔷凛)》之铭言：
课程名称︰微积分乙上
课程性质︰必带
课程教师︰王振男
开课学院：医学院
开课系所︰医学系
考试日期（年月日）︰2010/12/14
考试时限（分钟）：25
是否需发放奖励金：是
dy
1. Solve cosx (—) = 2 + 2ysinx, y(0) = 1.
dx
sol> dy/dx + (-2tanx)y = 2secx => I(x) = e^(-2∫tanx dx) = (cosx)^2
=> [(cosx)^2](dy/dx) + (-2(sinx)(cox)y) = d[y(cosx)^2]/dx = 2cosx
2(sinx + C)
=> y(cosx)^2 = 2∫cosx dx => y = ──────
(cosx)^2
y(0) = 1 => 2C/1 = 1 => C = 1/2 代回即可
2. Find the orthogonal trajectories for the family of curves
y^2 = cx^3 => y^2/x^3 = c
sol> 2y(dy/dx) = 3cx^2 => dy/dx = (3cx^2)/2y = 3y/2x
The orthogonal trajectories satisfy the differential equation
dy/dx = -2x/3y => 3y dy = -2x dx
=> ∫(1/3y) dy = ∫1/2x dx => (3/2)y^2 = -x^2 + C
=> (3/2)y^2 + x^2 = C
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※ 编辑: shokanshorin 来自: 140.112.4.200 (12/14 13:03)
1F：推 ALegmontnick:done 12/14 13:55
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※ 发信站: 批踢踢实业坊(ptt.cc)
◆ From: 114.24.153.162
2F：→ shokanshorin:强者我卷友!!! 12/15 23:29
3F：推 jech801127 :强者我同学! 12/15 23:44
4F：→ liltwnboiz :并没有 Orz 第五篇我还要再试试看...真难想... 12/15 23:47
5F：→ liltwnboiz :二楼凯杰? 12/15 23:47
6F：→ jech801127 :XD 我闻到浓浓的卷香!! 12/15 23:50
7F：推 ALegmontnick:人卷真好!!! 收进 12/16 00:37
8F：→ liltwnboiz :这篇有错 请小板主重新增加 感谢 12/23 22:04
※ 编辑: liltwnboiz 来自: 114.24.174.240 (12/23 22:30)