特征方程为r^5+r^4+2r³+2r²+r+1=0r^4(r+1)+r²(r+1)+(r+1)=0(r+1)(r^4+r²+1)=0(r+1)(r^4+2r²+1-r²)=0(r+1)(r²+r+1)(r²-r+1)=0得r=-1, (-1±i√3)/2, (1±i√3)/2故通解为:y=C1e^(-x)+e^(-x/2)[C2cos(√3x/2)+C3sin(√3x/2)]+e^(x/2)[C4cos(√3x/2)+C5sin(√3x/2)]