作者GBRS ()
看板trans_math
标题Re: [积分] 怎解
时间Fri Aug 11 19:39:43 2006
※ 引述《SeaBear ( 来乱的 )》之铭言：
: (dy/dt)+(y^2)=sint
: 怎解
: 查过题目没错
let sint=x
then d(sint)=dx
we have 1/dt=cost/dx=(1-x^2)^(1/2)/dx
take 1/dt=cost/dx=(1-x^2)^(1/2)dx to the equation
then we have (dy/dx)=x/(1-x^2)^(1/2)-(y^2)/(1-x^2)^(1/2)
it's a Riccati equation
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※ 发信站: 批踢踢实业坊(ptt.cc)
◆ From: 61.58.108.80
1F：→ RAINDD:不用令x=sin(t)，原方程式即满足Riccati-Eq 61.64.93.146 08/12 03:49
2F：→ GBRS:对厚~1F谢拉 61.58.108.80 08/12 10:53
3F：→ RAINDD:呐，楼上的高手，会解吗？想不出特解说... 61.64.93.146 08/12 13:25
4F：→ csfwing:这题特解难找,Riccati一定要找一个特解吗? 203.70.103.8 08/24 14:12
5F：→ GBRS:看了坊间许多微方书籍好像是如此... 61.56.185.167 08/27 20:05