[理工] 工數ode

[AAJJBurnett (叫我投手)]

                                                   at
 Consider the non-homogeneous linear system x'=Ax+e  v ,

 where x is a vector consisting of functions in t, a is

 not an eigenvalue of A ,and v不等於0 is a constant vector .

 Find a particular solution of the system,in terms of A,a,v and t.

                v   -at
 請問答案是 x= ----e      嗎 ?
               A-a

--
※ 發信站: 批踢踢實業坊(ptt.cc) 
◆ From: 140.114.206.124
推 doom8199:A 不是矩陣嗎?  (A-a) 怪怪的 XD
→ doom8199:假設特解是  x_p = C*exp(at) , 帶進去後會得到
→ doom8199:(A-aI)C = -v;  然後說明 (A-aI) 存在反矩陣後,C就可算了
→ doom8199:因此 x_p = -exp(at) *[(A-aI)^(-1)]v
→ AAJJBurnett:感恩感恩