課程名稱︰常微分方程導論
課程性質︰必修
課程教師︰陳宜良教授
開課學院：理學院
開課系所︰數學系
考試日期（年月日）︰10/30/07
考試時限（分鐘）：110分鐘
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1. Solve for the general solution of y'+(y/t) = cos(w*t) [10%]
2. Solve for the general solution of y'= (x^2+xy+y^2)/(x^2) [15%]
3. Classify the stability of equilibria (r is a real number) for
y' = ry(1-y^2); Explain your reasons [15%]
4. Solve the initial value problem y''-k^2y=g(t), y(0)=y'(0)=0
Represent your answer by a convolution integral. [15%]
5. Solve for the general solution of y''+(w^2)y = At + Bsin(w*t)
6. Find the orthogonal curves for (x/a)^2+(y/b)^2 = c, c>0
Find the differential equation represented by the curve [10%]
Solve the differential equation [5%]
7. Prove or disprove the following statement: for my''+ry'+ky =f(t), where
m, r, k >0, If y_p is a particular solution, any solution y satisfies
y-y_p -> 0, as t -> infinity [15%]
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※ 編輯: neomarkusan 來自: 218.166.239.20 (10/30 20:19)