课程名称︰工程数学二 课程性质︰土木系必修 课程教师︰杨德良 开课学院：工学院 开课系所︰土木系 考试日期︰2011年08月19日 考试时限：2:20-5:20，共180分钟 是否需发放奖励金：是 试题 : 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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