→ honestonly:噢 我忘記I.C.了 03/26 16:16
推 tedtedted:科 03/26 16:16
推 baoerking777:原來可以這樣算@@~我是用Laplace算 03/26 16:28
※ 引述《gn00648013 (大偉)》之銘言：
: Solve the system of differential equations as follow
: dx/dt=4x-2y
: dy/dt=x+y x(0)=6 y(0)=3
: ------------------------------------------------------
: Dx-4x=-2y . x(D-4)=-2y .......(1)
: Dy-y=x . y(D-1)=x ...........(2)
: y(D-1)(D-4)=-2y
: y(D-2)(D-3)=0 , y(t) = c1e^2t+c2e^3t
: 之後就卡住了= =.........
==============================================================
(D-4)x + 2y = 0 -------(1)
-x + (D-1)y = 0 -------(2)
由(2) ,x = (D-1)y 代入(1)
[(D-1)(D-4)]y + 2y = 0
2 2t 3t
(D - 5D + 6)y = 0 ,y = C1e + C2e 代回(1)
2t 3t 2t 3t 2t 3t
x = (D-1)y = 2C1e + 3C2e - C1e - C2e = C1e + 2C2e
故
2t 3t
x = C1e + 2C2e
2t 3t
y = C1e + C2e 為解
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