課程名稱︰工程數學一
課程性質︰必修
課程教師︰王昭男
開課學院：工學院
開課系所︰工程科學及海洋工程學系
考試日期（年月日）︰2009.12.10
考試時限（分鐘）：120
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題：
1. Find the eigenvalues and eigenvectors of the problem,
d 2x dy 2x
──(e ──) + e (λ+1)y = 0 ； 0 < x < π
dx dx
y(0) = 0
y(π) = 0
2. Use power series method (with center x= 0),find the solution of the
following equation：
2
(x -x)y"-xy'+y = 0
3. Find the general soluion of the nonhomogenous equation：
┌ ┐ ┌ 2 ┐
│ 2 -4 │ │ t + 2t │
y'= Ay + g = │ │y + │ 2 │
│ 1 -3 │ │ t +t+3 │
└ ┘ └ ┘
4. If the general solution of the Bessel's equation
2 2 2
x y" + xy'+ (x - ν )y = 0 can be expressed by Bessel function
y(x)= AJ(x) +BY(x)
ν ν
Find the general solution (in terms of the Bessel function) of the
equatuon：
2 2 2ν 2
x y"+(1-2ν)xy'+ν(x +1-ν)y = 0
-ν ν
Hint: u = x y z = x
5. Find the critical points and its type of the following equation of
3
y"+y'-4y+y = 0
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※ 編輯: fong1014 來自: 61.217.60.85 (12/15 12:10)