[理工] [工數]-請教三題ODE

看板Grad-ProbAsk作者Tonyy (Cool)時間16年前 (2009/11/15 18:43)推噓8(8推 0噓 5→)

留言13則, 9人參與討論串1/3 (看更多)

1. < 周易工數2-2第五題 > let y1(x) y2(x) be two solution of y''(x) + p(x)y'(x) + q(x)y(x) = 0 y(0) = 1 Then , (A) y1(x) + y2(x) is also a solution (B) y1(x) * y2(x) is also a solution (C) y1(x) / y2(x) is also a solution (D) none 答案是 (D) 不過我覺得應該是 (A) 不曉得這題怎麼想 ? 2. < 周易工數2-2第六題 > consider the following initial value problem d^2 x + 2 dx + x ____ ____ = 0 x(0) = 1 ; x'(0) = c dt^2 dt where c is a parameter . find the range of c within which all solution of the given initial value problem are non-negtive ,that is , determine all possible values of c which yield x(t) > 0 for t > 0 = = 答案是 : c > -1 這題大意上就是要找 c 的範圍使得ODE中的 x(t) 恆大於等於 0 ( 當 t 大於等於0 ) 不過我算了很多次還是不太對不知怎麼解才對 ? 3. < 周易工數2-6第十六題 > y'' - 3y' - 4y = x^-3 (5x-2) e^4x 答案 : y = c1 e^-x + c2 e^4x - x^-1 e^4x 希望有會的人可以解惑一下謝謝 !! -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 114.27.208.226

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yimao

11/15 18:48, , 1^F

11/15 18:48, 1^F

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fonlintw0621

11/15 18:55, , 2^F

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fonlintw0621

11/15 18:55, , 3^F

11/15 18:55, 3^F