高数微分方程求解

2025-05-18 10:58:07
推荐回答(1个)
回答(1):

特征方程为r^5+r^4+2r³+2r²+r+1=0
r^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)]