[试题] 109上 夏俊雄 常微分方程导论 第二次期中

楼主: t0444564 (艾利欧)   2020-12-08 13:50:46
课程名称︰常微分方程导论
课程性质︰数学系大二必修
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︰2020年11月17日(二),15:30-18:30
考试时限:180分钟
试题 :
              ODE EXAM 2 11/17/2020
1. (20 points) Set
(3 1 -2)
               A = (2 4 -4),
(2 1 -1)
T
X(t) = (x1(t),x2(t),x3(t)) and g(t) = (t,cos(t),sin(t)). Solve the
differential system
             X'(t) = AX(t) + g(t)
T
with initial condition X(0) = (1,2,3) .
2. (10 points) Find the solution of the initial value problem
2y'' + y' + 3y = δ(t-5)
with initial condition y(0) = 0, y'(0) = 0.
3. (20 points) Solve the following two integro-differential equations
1 t 2
ψ'(t) -

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