Re: [工數] 解微分方程使用Fourier傅立葉 及 Lapla …
※ 引述《StevnCurry (Sap)》之銘言：
: 題目是這樣的
: -2t
: y'-2y = u(t)exp
: 若用lapalce解 令L{y} = Y(s)
: 2t -2t 2t
: => y(t) = (1/4){ e - e }+ c{e }
: 若用fourier解 令F{y} = Y(w)
: -2|t|
: => y(t) = (-1/4)e (這是課本的標準解答)
: why ?
because f(t)=u(t) e^{-2t} is DISCONTINUOUS at t=0
the fourier intergral solution y(t) will be such that
y'(0)-2y(0)=[f(0+)+f(0-)]/2
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 112.104.170.244
推
08/17 13:02, , 1F
08/17 13:02, 1F
→
08/17 13:03, , 2F
08/17 13:03, 2F
→
08/17 13:04, , 3F
08/17 13:04, 3F
→
08/17 13:04, , 4F
08/17 13:04, 4F
Your solution is not General,
because f(0) is NOT defined.
I just can solve TRIVIAL problem.
※ 編輯: JohnMash 來自: 112.104.170.244 (08/17 13:07)
討論串 (同標題文章)