Re: [理工] [工數]-簡單ODE ~"~
※ 引述《topee (eason)》之銘言：
: dy 1
: ---= ------
: dx x+y+1
: (x+y+1)dy-dx=0
: 令u=x+y . y =u-x . dy=du-dx
->y'=u'-1
1
u'-1=------
u+1
u+2
u'=--------
u+1
u+1
---du=dx .............(4)
u+2
中間會嗎?= =
1
(1 - ----)du=dx .............(5)
u+2
就只是積分...
u - ln(u+2)=x+c1 ............(6)
x+y-ln(x+y+2)=x+c1
y-c1=ln(x+y+2)
ce^y=x+y+2
x=ce^y-(y+2)
其實看簡單點
顛倒過來是很熟的一階線性唷^^
->
x+y+1=dx/dy=x`
x`-x=y+1
同乘I=e^-y
e^-y(x`-x)=e^-y(y+1)
xe^-y=∫e^-y(y+1)dy
=-e^-y(y+2)+c1
x=c1e^y-(y+2)
應該沒算錯吧Q_q
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※ 編輯: iyenn 來自: 123.193.214.165 (04/12 23:52)
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