[理工] 工數
用拉式解ODE
y'' + y' + y=δ(t-1)
3^1/2 3^1/2 1
ans:cos(--------) e^(-t/2) + sin(-------) -------- e^(-t/2) +
2 2 3^1/2
3^1/2
e^(-t/2 -1) --------- sin 3^1/2(t-1) u(t-1)
2
拉式轉換
6S+18+S^4
f(t)=t^3 +e^(-3t) =---------------
S^4(S+3)
f(t)=5δ(t-3) = 5e^-3s
反拉式
2
F(s)=--------- = 2t e^2t
s^2 -2
e^-2s
F(s)=------------ = e^(-t-2) cos 2(t-2) u(t-2)
s^2 +2s-5
gamma function x= -1/2 要怎做???
請大家幫我檢查一下答案是否正確!!
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