課程名稱︰工程數學上
課程性質︰系定必修
課程教師︰蕭浩明
開課學院：工學院
開課系所︰機械工程學系
考試日期（年月日）︰2009/12/14
考試時限（分鐘）：130分鐘
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
-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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