课程名称︰工程数学-微分方程
课程性质︰大二必修
课程教师︰管杰雄
开课学院：电资学院
开课系所︰电机工程学系
考试日期（年月日）︰2014/11/26
考试时限（分钟）：130分钟
试题 :
Midterm Examination of Differential Equations, FALL, 2014
AM 10:20 ~ PM 12:30, 26th November, 2014
Find the solutions of following differential equations
1. (20%)
4y" + 36y = csc(3x)
2. (20%)
x^2+y^2 y^2-1 (y^2-1)(x^2+y^2)
(y')^2 + ( ────── - ──── )y' - ────────── = 0
x^2-xy x x^3-(x^2)y
(Hint : Find the normal form of the equation)
3. (20%)
[(y^-1)siny-sinx]dx + [(x/y)cosy+(y^-1)cosx]dy = 0
4. (20%)
y" - 5y" + 6 = e^(2x) + cosx, if x>=0
y" + y' -6 = e^(2x) +cosx, if x<0
the domain is (-∞,∞).
(Hint : Need to consider that y = y(x) and y' = y'(x) are continuous at x=0.)
5.(20%)
(x^2)y''' - (2x+x^2)y" + (2+2x)y' -2y = 0
(Hint : (i) Guess a solution,
(ii) Accorading to the guessing solution, find the relative
first-order differential operator or differential equation,
(iii) To find the other second-order differential operator or
differential equation. )