方程y″－3y′＋2y＝excos2x的特解形式y*＝（　　）。 -题库考试答案搜索网

方程y″－3y′＋2y＝excos2x的特解形式y*＝（　　）。

单选题

2022-02-23 13:33

A、Ae<sup>x</sup>cos2x
B、xe<sup>x</sup>（Acos2x＋Bsin2x）
C、e<sup>x</sup>（Acos2x＋Bsin2x）
D、x<sup>2</sup>e<sup>x</sup>（Acos2x＋Bsin2x）

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正确答案

C

试题解析

原方程对应齐次方程的特征方程为r²－3r＋2＝0，解得r₁＝1，r₂＝2。显然1±2i不是特征方程的根，则其特解形式为e^x（Acos2x＋Bsin2x）。

标签：考研公共课数学军队文职专业科目

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