[理工] 工數 Laplace ODE
Use the Laplace transform to solve the differential equation:
ty''+(4t-2)y'-4y=0 ; y(0)=1
我解到
s^7
Y= ∫ ------- ds 就卡住了
(s+1)^5
變數變換令(s+1)=t應該有辦法積出來
但這個積分有比較快的方法積出來嗎?
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我腦殘算錯了， 算出來
(s+4)+2 c 1 1 1 1
Y(s)=-------- + ----[----- + -------- - ---- + -------- ]
(s+4)^2 16 s^2 (s+4)^2 2s 2(s+4)
反拉
-4t -4t c -4t 1 1 -4t
y(t)=e + 2te + ----[t + te - --- + ---e ]
16 2 2
※ 編輯: cg1436 來自: 61.57.78.145 (02/10 23:15)
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