課程名稱︰微分方程
課程性質︰系定必修
課程教師︰統一教學
開課學院：電資學院
開課系所︰電機系
考試日期（年月日）︰97/11/12
考試時限（分鐘）：10:20~12:50
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1.(5%)看圖題 給一個函數y''+ y = f(x)的圖形
須從六個選項中選出符合的解 並簡敘理由(不必解微方)
2.(7%)Solve y'= y^2 - 9
1
3.(10%)Solve y'= ─────
(x + y^2)
4.(8%)Solve x(x+y)^2 dx + (2x^2 y + x^3 -x )dy = 0, y(1) = 1
5.(10%)Solve 2(3y^2 - t^2)dy + tydt =0
6.(10%)Solve y''-3y'+ 2y = 3exp(-x), y(0) = 1, y'(0) = 0
7.(10%)Solve x^2 y''- 5xy'+ 10y = 0 for x < 0
dx
── = 4x - 3y
dt
8.(15%)Solve with x(0) = 2, y(0) = -1
dy
── = 6x - 7y
dt
9.(10%)Consider the boundary-value problem y''+λy = 0, y(0) = 0, y(π/2) = 0
Discuss: Is it possible to determine values of λ so that the problem
possesses (a) trivial solutions? (b) nontrivial solutions?
10.(20%)Solve the given initial-value problem and give the largest interval I
on which the solution is defined.
(a)(5%) y(lnx - lny)dx = (x lnx - x lny - y)dy, y(1) = 1
(b)(5%) xy'= y ln(xy), y(1) = 1
(c)(5%) xy(y') + y^2 =32x, y(1) = 1
(d)(5%) y''- y = cosh(x), y(0) = 2, y'(0) = 12
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