下列函数中，可作为某二阶微分方程的通解的是（　　）。 -题库考试答案搜索网

下列函数中，可作为某二阶微分方程的通解的是（　　）。

单选题

2022-02-24 18:05

A、y＝c<sub>1</sub>x<sup>2</sup>＋c<sub>2</sub>x＋c<sub>3</sub>
B、x<sup>2</sup>＋y<sup>2</sup>＝c
C、y＝ln（c<sub>1</sub>cosx）＋ln（c<sub>2</sub>sinx）
D、y＝c<sub>1</sub>sin<sup>2</sup>x＋c<sub>2</sub>cos<sup>2</sup>x

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正确答案

D

试题解析

A项中，含有三个独立的任意常数，则A项为三阶微分方程的通解；B项中，含有一个独立的任意常数，则B项为一阶微分方程的通解；C项中，因为y＝ln（c₁cosx）＋ln（c₂sinx）＝ln|c₁|＋ln|c₂|＋ln|cosx|＋ln|sinx|＝c＋ln|cosx|＋ln|sinx|。故C项中含有一个独立的任意常数，则C项为一阶微分方程的通解。

标签：考研公共课数学军队文职专业科目

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