作者birdhackor (夜残狼)
看板Grad-ProbAsk
标题Re: [理工] [工数]-高阶ODE Euler cauchy方程
时间Thu Dec 10 01:26:00 2009
: 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
∫--------------dx 令x=tan(p)
x^2(x^2+1)^3/2
1
=∫-------------------sec^2(p)dp
tan^2(p)*sec^3(p)
cos^3(p)
=∫----------dp
sin^2(p)
cos^2(p)
=∫----------d[sin(p)]
sin^2(p)
1-sin^2(p)
=∫------------d[sin(p)]
sin^2(p)
1
=∫----------d[sin(p)] -∫ 1 d[sin(p)]
sin^2(p)
= -[sin(p)]^(-1) - sin(p)
-x -(1+x^2)^(1/2)
= ------------- + ----------------
(1+x^2)^(1/2) x
-(1+2x^2)
= -----------------
x*(1+x^2)^(1/2)
不用IBP的方式
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1F：推 CRAZYAWIND:真强....... 12/10 01:48
※ 编辑: birdhackor 来自: 140.116.91.47 (12/10 12:11)