课程名称︰常微分方程导论
课程性质︰必修
课程教师︰夏俊雄
开课学院：理学院
开课系所︰数学系
考试日期（年月日）︰2012/12/11
考试时限（分钟）：
试题 :
ODE QUIZ 6 12/11/2012
1. Find the range of μ ∈ R at which the van der Pol equation
u'' - μ(1 - u^2)u' + u = 0
has time periodic solutions.
2. Find the inverse Laplace transform for each of the following functions.
2 3 5(s + 1)
f(s) = ────── + ────── + ──────
(s + 2)^4 s^2 + 16 s^2 + 2s + 5
3s + 1
g(s) = ─────────.
(s^2 - 4s + 20)
3. Find the general power series solution for the Airy's equation
y'' - xy = 0, -∞ < x < ∞.
What is the radius of convergence of the solution you obtain?
4. Do you think the following equations have periodic solutions? Prove or
disprove it.
x'' + x - x^2 = 0,
x'' + x^3 + x^4 = 0.