課程名稱︰常微分方程導論
課程性質︰系必修
課程教師︰林紹雄
開課學院：理學院
開課系所︰數學系
考試日期（年月日）︰2010年10月12日
考試時限（分鐘）：50分鐘
是否需發放獎勵金：是
試題 :
There are problems A to B with a total 50 points. Please write down your comp-
utational or proof steps clearly on the answer sheets.
A. Solve the following ODE.
(a) (10 points) y''' - 4y' = 2t + 3(cos t)^2 +e^(-2t)
y(0) = 0 , y'(0) = -1 , y''(0) = 0.
(b) (20 points) The homogeneous equation ty'' + (5t-1) y' - 5y = 0 has a solu-
tion of the form y1(t) = at +b. Then solve the inhomogeneous equation
ty'' + (5t-1)y' -5y = t^2 * e^(-5t)/
(c) (8 points) (t^3)y''' + (t^2)y'' - 2ty' + 2y = 0 in t > 0.
B.It is known that t,t^2 and t^3 are three solutions of the ODE y'' +p(y)y' +
q(t)y = f(t).
(a) (7 points) Find a basis of solutions for the corresponding homogeneous eq-
uation. Then solve the ODE with initial conditions y(2) = 2 ,y'(2) = 5.
(b) (5 points) Find p(t) explicitly.
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 140.112.251.220