作者kagato (包)
看板Grad-ProbAsk
标题Re: [理工] [工数]-高阶ode
时间Thu Dec 17 00:40:16 2009
※ 引述《winer8 (快来明星3 缺1 )》之铭言：
: 2 2
: 1. yy"-(y') -y y'=0
y^2(y'/y)' - y^2 y' = 0 , (y'/y)' - y' = 0 ,y'/y -y = c1
dy y
y' = y^2 + c1y , ___________ = dx ,1/c1 ln____________ = x + c2
y(c1+y) y+c1
: c1
: ans: y= ----------------
: c2exp(-c1x) -1
: 2. x"-2x'+3y'+2y=4
: 2y'-x'+3y=0 x(0)=y(0)=x'(0)=0
let L{x(t)}=X(s) , L{y(t)} = Y(s)
(s^2-2s)X + (3s+2)Y = 4/s
- sX + (2s+3)Y = 0
-3 -7/2 1/6 10/3 -1 2/3 1/3
X = ___ + ____ + ___ + _____ , Y= ___ + ___ + ____
s^2 s s+2 s-1 s s-1 s+2
x,y = ..
: 10 t 1 -2t 7 2 t 1 -t
: ans: x=----e +-----e -3t- ---- y=-----e +----e -1
: 3 6 2 3 3
: 3. z"+y'=cosx y"-z=sinx z(0)=-1 z'(0)=-1 y(0)=1 y"(0)=0
z'''+y'' = -sinx , y'' = -sinx - z'''
-sinx - z''' - z = sinx , z''' + z = -2sinx => z = -sinx - cosx
: y=cosx z=-sinx-cosx
: 感谢各位了
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※ 编辑: kagato 来自: 118.171.74.171 (12/17 01:08)