设函数y1(x),y2(x),y3(x)都是线性方程y''+P(x)y'+Q(x)y=f(x)的特解,其中P,Q,f都是

y=(1-C1-C2)y1(x)+C1y2(x)+C2y3(x)
即
y=y1(x)+C1*[y2(x)-y1(x)] +C2*[y3(x)-y1(x)]
而y1(x),y2(x),y3(x)都是线性方程y''+P(x)y'+Q(x)y=f(x)的特解
所以
y2(x)-y1(x)和y3(x)-y1(x)就都是对应的齐次方程y''+P(x)y'+Q(x)y=0的通解
而y1(x)是y''+P(x)y'+Q(x)y=f(x)的特解
所以
y=(1-C1-C2)y1(x)+C1y2(x)+C2y3(x)
=y1(x)+C1*[y2(x)-y1(x)] +C2*[y3(x)-y1(x)]
一定是方程的通解,选择D