作者Derver (木律)
看板NTU-Exam
标题[试题] 100上 徐治平 工程数学 期中考
时间Fri Nov 25 16:04:04 2011
课程名称︰工程数学一
课程性质︰必修
课程教师︰徐治平
开课学院：工学院
开课系所︰化工系
考试日期（年月日）︰2011.11.25
考试时限（分钟）：10:20~12:20
是否需发放奖励金：是
（如未明确表示，则不予发放）
试题 :
1.Find the general solution of the following differential equations by power
series method (25% each)
a.y'' + (sinx)y = e^(x^2) (at least up to x^4)
b.(1+x^2)y'' - y' + y = 0 (at least up to x^4)
c.y'' + (λ^2)y = 0 (at least up to x^5)
2.Consider solving the differential equation below by power series method
(x^2)y'' + x(1/2 + 2x)y' +(x - 1/2)y = 0
a.Show that zero is a regular singular point (5%)
b.Find and solve the indicial equation (5%)
c.Determine the recurrence relation (5%)
d.Use the results obtain in band c to find the first four nonzero terms of the
linearly independent Frobenius solutions (10%)
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