Re: [理工] [ODE]

看板Grad-ProbAsk作者honestonly (感冒了~哭哭)時間15年前 (2010/03/26 16:10)推噓2(2推 0噓 1→)

留言3則, 3人參與討論串6/17 (看更多)

※ 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 -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 118.167.134.174

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honestonly

03/26 16:16, , 1^F

03/26 16:16, 1^F

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tedtedted

03/26 16:16, , 2^F

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baoerking777

03/26 16:28, , 3^F

03/26 16:28, 3^F