[試題] 101-1 夏俊雄 常微分方程導論 第二次小考

[Malzahar (虛空先知)]

課程名稱︰常微分方程導論
課程性質︰必修
課程教師︰夏俊雄
開課學院：理學院
開課系所︰數學系
考試日期（年月日）︰2012/09/14
考試時限（分鐘）：

試題 :

                              ODE QUIZ 2  9/14/2012

1.
                      ╭ 1  1╮        ╭1   1╮        ╭ 1  2╮
                  A = │     │,   A = │     │,   A = │     │,
                      ╰-1  3╯        ╰0   3╯        ╰-2  1╯
For each of the above matrices A ∈ M_2(R), solve the differential equation

                                dx(t)
                               ──── = Ax(t),
                                  dt

                                   T
with initial condition x(0) = (1,2) .

2. Solve the following differential equations:

   a)                  y'(t) = sin(t)y,   y(0) = y_0,

   b)                  y'(t) - 2y = 4 - t,  y(0) = 6.

3. Suppose a-1 = 1. a_2 = 3. For  each of the following cases, express a_n as a
function of n, for n = 1,2,3,….

   a) a_n = 3a_n-1 + 3a_n-2 for n≧3.

   b) a_n = 2a_n-1 - a_n-2 for n≧3.

   c) a_n = a_n-1 + a_n-2 for n≧3.


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※ 編輯: Malzahar (118.166.208.171), 02/12/2015 17:02:09
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