Re: [理工] [工數]- 白努力!! 可以幫忙檢查一下 …
※ 引述《topee (eason)》之銘言：
: y'-y = y^2
: dy-ydx=y^2dx
: 除y^2
: y^-2dy - y^-1dx = dx
: 令u= y^1-2 =y^-1
: du = (1-2)y^-2dy
: -du-udx = dx
: du+udx = -dx
: (D+1)u = -1
: u = c1e^-x
: h
: u = (1-D)(-1)
: p
: = -1
: 1/y = c1e^-x-1
: y=(c1e^-x-1)^-1
y^-2 y' - y^-1 = 1
let u = y^-1 u' = -y^-2 y'
-u' - u = 1
u' + u = -1 I=e^∫1dx = e^x
e^x u = ∫- e^x dx + c
e^x y^-1 = -e^x + c
y^-1 = c e^-x - 1
y = ( c e^-x - 1 )^-1
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