作者laba888 (喇叭)
看板NTU-Exam
标题[试题] 98上 萧浩明 工程数学上 第2/2次期中考
时间Mon Dec 21 20:24:21 2009
课程名称︰工程数学上
课程性质︰系定必修
课程教师︰萧浩明
开课学院：工学院
开课系所︰机械工程学系
考试日期（年月日）︰2009/12/14
考试时限（分钟）：130分钟
是否需发放奖励金：是
（如未明确表示，则不予发放）
试题 :
-t t
1. Solve L[e ∫ tsin2tdt] (10%)
0
-2t
2. Solve L[te sinwt] (10%)
-1 1 1
3. Given that L [───────] = ──[2sint-sin2t] (10%)
4 2 6
s + 5s + 4
2
-1 2s - s + 1
Find L [───────]
4 2
s(s + 5s + 4)
4. Use Laplace Transform to solve y"-4ty'+4y = 0; y(0) = 0,y'(0) = 10 (10%)
5. Use Laplace Transform to solve y"+2y'+y = f(t); y(0) = 0, y'(0) = 0 (15%)
f(t)
1├
────
│ │ │
│
─┼
───┴───┴───┴
───┴───┴─ t
│ 1 2 3 4 5
│ │ │
-1├
────
囧mmmmmm~ 希望看得懂
6. Use Laplace Transform to solve the system of differential equation
╭ x'(t) - 4x + y'''(t) = 6sint
┤
╰ x'(t) + 2x - 2y'''(t) = 0
x(0) = 0, y(0) = 0, y'(0) = 0, y"(0) = 0 (15%)
7. Use Taylor Series Method to solve y"- xy' + y = 0 (10%)
6
(expanded to x )
8. Find the recurrence formula and general solution near x = -1 for the
differential equation y" + xy' + (2x-1)y = 0 (15%)
4
(expanded to (x+1) )
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