作者ying11027 (怀念)
站内NTU-Exam
标题[试题] 98上 陈俊全 常微分方程导论 期末考
时间Thu Jan 14 16:00:14 2010
课程名称︰常微分方程导论
课程性质︰数学系必修
课程教师︰陈俊全
开课学院：理学院
开课系所︰数学系
考试日期（年月日）︰2010/01/04
考试时限（分钟）：110分钟
是否需发放奖励金：是
（如未明确表示，则不予发放）
试题 :
Choose 4 from the following 6 problems.
(4)
1. Solve the equation y + 2 y'' + y = 3sin3t.
2. Use the Laplace transform to solve the equation
(4)
y - y = δ(t - 2) , y(0) = y'(0) = y''(0) = y'''(0) = 0
3. Use the method of reduction of order to find a second solution of the
eqution
(x - 1)y'' - xy' + y = 0, x > 1 ; y1(x) = expx
4. Find the general solution of the linear system
( -8 -1 0 )
x'(t) = ( 16 0 -1 ) x(t)
( 0 0 1 )
5. Find the solution of the linear system
( 2 1 ) ( t ) ( 1 )
x'(t) = (-5 -2 ) x(t) + ( 3 ), x(0) = ( 2 )
6. Let L{f(t)}(s) denote the Laplace transform of f(t). Suppose L{f(t)}(s) and
L{g(t)}(s) both exist for s > a ≧ 0. Prove that L{h(t)} = L{f(t)}L{g(t)}
for s > a, where t
h(t) = ∫ f(t - σ)g(σ) dσ
0
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