课程名称︰常微分方程导论 课程性质︰系必修 课程教师︰林绍雄 开课学院：理学院 开课系所︰数学系 考试日期（年月日）︰2010年10月26日 考试时限（分钟）：50分钟 是否需发放奖励金：是 试题 : There are problems (a) to (b) with a total of 50 points. Please write down yo- ur computational or proof steps clearly on the answer sheets. A real 4 ×4 matrix A has characteristic polynimial (x^2 +2x +2)^2. Its eigen- value -1+i (where i = (-1)^(1/2)) has generalized eigenvectors given by [ 1+i ] [ 1+i ] w1 = [ i ] , w2 = [ 1+i ] [ 0 ] [ 1+i ] [ 0 ] [ i ] so that Aw1 =(-1 + i)w1 and Aw2 = (-1+i)w2 + w1. (a) (35 points) Write down a real basis for the solution space of the homogen- eous equation y' = Ay. (b) (15 points) Consider the inhomogeneous equation y' = Ay + we^(-t)(cos t), where w ∈ R^4. What form of a particular solution is given by the method of undetermined coeffcients? --

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