推 initialpp : 先謝謝大大，忘了說有IC xD 05/17 00:39
→ initialpp : y(0)=0,y'(0)=0 05/17 00:39
※ 引述《initialpp (沒檔頭)》之銘言：
: 又卡題，求大大幫忙，先謝過!!
: y"+5y'+6y=?(t-1/2ㄦ)+u(t-ㄦ)cos t
: ?=delta
: ㄦ=拍，就是3.14那個拍..
: (以上兩個符號我打不出來ㄅ歉)
: 再次謝過~~
y" + 5y' + 6y = δ(t - π/2) + u(t - π)cos(t)
設y(0) = a, y'(0) = b
[Ys^2 - sa - b] + 5[Ys - a] + 6Y = exp(-sπ/2) - exp(-sπ)s/(s^2 + 1)
[s^2 + 5s + 6]Y = as + 5a + b + exp(-sπ/2) - exp(-sπ)s/(s^2 + 1)
1 1
Y = [------ _ -----][as + (5a + b) + exp(-sπ/2) - exp(-sπ)s/(s^2 + 1)]
s + 2 s + 3
a(s + 5/2) + (5a + 2b)(1/2) + 2(1/2)exp(-sπ/2)
= --------------------------------------------------
(s + 5/2)^2 - 1/4
exp(-sπ) s
+ ---------------------------
s^2 + 1
=> y(t) = a exp(5t/2) cosh(t/2) + (5a + 2b) exp(5t/2) sinh(t/2)
+ 2 u(t - π/2)exp(5t/2) sinh(t/2) + cos(t) u(t - π)
--
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