設(shè)y=mcos(x/2)+nsin(x/2)+C(x)e^3x
y'=(-m/2)sin(x/2)+(n/2)cos(x/2)+(C'+3C)e^3x
y''=(-m/4)cos(x/2)+(-n/4)sin(x/2)+(C''+3C'+3C'+9C)e^3x
-m/4=1 -n/4=0 C''+6C'+9C=1
m=-4
C''+6C'+9C-1=0
C''+6C'+9(C-1/9)=0
(C-1/9)''+6(C-1/9)'+9(C-1/9)=0
特征方程
r^2+6r+9=0
r=-3
C-(1/9)=C1e^(-3x)
C(x)=C1e^(-3x)+1/9
通解y=(-4)cos(x/2)+(1/9)e^3x+C1