課程名稱︰工程數學一
課程性質︰必修
課程教師︰徐治平
開課學院：工學院
開課系所︰化工系
考試日期（年月日）︰2011.11.25
考試時限（分鐘）：10:20~12:20
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
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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