已知y1(x)和y2(x)是方程y''+p(x)y'+Q(x)y=0的两个线性无关的特解,Y1(x)和Y2(x)分别是方程y''+p(x)y'+Q(x)y=R1(x)和y''+p(x)y'+Q(x)y=R2(x)的特解。那么方程y''+p(x)y'+Q(x)y=R1(x)y+R2(x)的通解应是:

题目类型: 单选题

题目内容

已知y1(x)和y2(x)是方程y''+p(x)y'+Q(x)y=0的两个线性无关的特解,Y1(x)和Y2(x)分别是方程y''+p(x)y'+Q(x)y=R1(x)和y''+p(x)y'+Q(x)y=R2(x)的特解。那么方程y''+p(x)y'+Q(x)y=R1(x)y+R2(x)的通解应是:

题目选项

A. c1y1+c2y2
B. c1Y1(x)+c2Y2(x)
C. c1y1+c2y2+Y1(x)
D. c1y1+c2y2+Y1(x)+Y2(x)

正确答案

D

题目解析

提示:按二阶线性非齐次方程通解的结构,写出对应二阶线性齐次方程的通解和非齐次方程的一个特解,得到非齐次方程的通解。

题目纠错