[理工] [工數] 聯立ODE
請問大家
關於
X'=AX
A= [ 1 3 , -3 7]
它的特徵值
4 , 4
E1= c1 [1 ,1]^T
E2要用廣義特徵向量去作 弄出來是 [1 , 4/3]^T
寫解答時
c1 E1 e^4t + c2 { E1 t e^4t +E2 e^4t}
如果小弟用
e^At = aA+bI
e^4t = a4+b
te^4t= a
----> a=te^4t and b=e^4t-4te^4t
e^At= aA+bI = te^4t [ 1 3 , -3 7] + {e^4t -4te^4t} [1 0, 0 1]
整理後
答案是
[e^4t -3te^4t 3te^4t , -3te^4t 3te^4t+e^4t]
答案好像跟上面那個不一樣
請問原因是因為廣義特徵向量那裏取法不同導致不一樣嗎??
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