课程名称︰常微分方程导论
课程性质︰必修
课程教师︰夏俊雄
开课学院：理学院
开课系所︰数学系
考试日期（年月日）︰2012/09/14
考试时限（分钟）：
试题 :
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.