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）︰2012/10/12
考試時限（分鐘）：
試題 :
ODE QUIZ 5 10/12/2012
1. Solve the following differential equations.
(4)
y + 5y'' + 4y = 1 - u_π(t), y'''(0) = y''(0) = y'(0) = y(0) = 0.
y'' + y = u_4π(t), y(0) = 1, y'(0) = 0.
2.Find the inverse Laplace transform for each of the following functions.
9s + 6
f(s) = ───────────,
(s + 2)(s - 2)(s + 1)
s^3 - 2s^2 - 6s - 6
g(s) = ──────────.
(s^2 + 2s + 2)s^2
3. Solve the following problems by power series.
y'' - xy' -y = 0, y(0) = 2, y'(0) = 1.
(2 + x^2)y'' - xy' + 4y = 0, y(0) = -1, y'(0) = 3.
(1-x)y'' + xy' - y = 0, y(0) = -3, y'(0) = 2.