课程名称︰微分方程 课程性质︰系定必修 课程教师︰统一教学 开课学院：电资学院 开课系所︰电机系 考试日期（年月日）︰97/11/12 考试时限（分钟）：10:20~12:50 是否需发放奖励金：是 （如未明确表示，则不予发放） 试题 : 1.(5%)看图题 给一个函数y''+ y = f(x)的图形 须从六个选项中选出符合的解 并简叙理由(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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