課程名稱︰工程數學一
課程性質︰必修
課程教師︰李克強
開課學院：工學院
開課系所︰化工系
考試日期（年月日）︰2011/11/18
考試時限（分鐘）：110min(後延長至130min)
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
(一) Solve the following ODEs (50%, 5% each)
dy - 1
1.(----) = xy^3(1 + x^2)^(-----)
dx 2
x
2.dx + (--- - siny) = 0
y
dy y^2 + 2xy
3.(----) = -----------
dx y^2
dy
4.(----) + xy = xy^2
dx
5.y'y" = 2, y(0)=1, y'(0)=2
6.y"+4y'+5y = 0, y(0)=1, y'(0)=0
7.y"-3y'-4y = e^(-x)
8.y"+2y'+y = e^(x)cosx
9.y'''+y' = 0, y(0)=0, y'(0)=1, y"(0)=2
10.y'''-2y"-y'+2y = e^(4x)
(二) Verify that e^(x) abd x are solutions of the homogeneous equation
corresponding to (1-x)y"+xy'-y = 2(x-1)^(2)e^(-x), and find the general
solution. (10%)
(三) Find the solution of the following problems. (40%, 10% each)
1.y"+2y'+y = f(t),
1. 0≦t< 1
f(t){ }, y(0)=0 , y'(0)=1
0, t≧1
2.y"+3y'+2y = u(t-2), y(0)=0, y'(0)=1,
where u(t-2) is a unit step function.
3.y"-y=2δ(t-1), y(0)=1, y'(0)=0,
where δ(t-1) is an impulse function.
4.f(t) = 2t^(2) +∫f(t-τ)e^-(τ)dτ, τ[0,t](上下限範圍)
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※ 編輯: tsf73 來自: 140.112.22.94 (11/18 15:27)