課程名稱︰工程數學二
課程性質︰土木系必修
課程教師︰楊德良
開課學院：工學院
開課系所︰土木系
考試日期︰2011年08月19日
考試時限：2:20-5:20，共180分鐘
是否需發放獎勵金：是
試題 :
Engineering Mathematics II
2011/8/19 2-5pm
professor DL Young
1st Mid-Term Exam
2011 summer session II
problems 1-4 (10%)
problems 5-8 (15%)
2 dy 4
1. Solve x ---- -2xy = 3y
dx
3 2 4 2
2. Solve (4t y - 15t -y)dt + (t +3y -t)dy = 0
dy xy+3x- y-3
3. Solve ---- = ------------
dx xy-2x+4y-8
dy 2
4. given ---- = y (4 - y^2)
dx
(a) find the critical points and phase portrait of the given autonomous
first-order differential equation.
(b) Classify each critical point as asymptotically stable, unstable, or
semi-stable.
(c) By hand, sketch typical solution curves in the regions in the xy-plane
determined by the graphs of the equilibrium solutions.
5. Solve IVP y'' + y = 4x + 10sin(x) , y(π)=0 , y'(π)=2
6. Solve BVP (x^2)y'' + xy'- y = ln(x) , y(1)=0 , y(2)=0
7. Solve IVP y''-2y'+10y = g(x) , y(0)=0 , y'(0)=0
g(x) = 20 , 0<=x<=π
0 , x>π
8. Solve BVP (x^2)y'' - 2xy + 2y = 3x^2 , y(1)=0 , y'(2)=0
by the method of Green's function
That is
(a) find tje Green's function G(x,t)
(b) use Green's function to solve y
(c) If you are able to solve the same problem by other method, I will give
you some credit.
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