噓 Sony:我們不迎合市場需求 我們創造市場需求...
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課程名稱︰工程數學一
課程性質︰系定必修
課程教師︰楊馥菱
開課學院：工學院
開課系所︰機械工程學系
考試日期（年月日）︰20081104
考試時限（分鐘）：70
是否需發放獎勵金：是
試題 :
Ⅰ. 1st order ODE (10%+10%+10%+10%)
1. xy' = 2x + 2y, y(1) = 0
dy
2. 4x + 8y─ = 0, y(1) = 2. Is this ODE exact?
dx
2
-1 x
3. y' + x y = 2e , y(1) = e
3 2 2 y dy
4. (2xy + 4) + (3x y + e )─ = 0, y(1) = 0. Is this ODE exact? If yes,
dx
determine the function ψ(x,y) that implicitly contains the solution to
the ODE.
Ⅱ. 2nd order ODE (10%+10%+15%+15%)
5. y" + y = cos(x), y(0) = -1 & y'(0) = 1
2 27
6. y" - 4y' + 13y = 26x + ─
13
x
7. y" - 2y' + y = e + x
2 ＿＿
8. x y" + 2xy' - 12y = √(x)
-x
9. y" + 2y' + y = e ln(x) for x > 0
n ｄ n+1 n+1
To solve∫x ln(x)dx, try to back calculate from ─(ax ln(x) - bx )...
dx
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