Question

常微分方程特征根是复重根，通解怎么写

我解方程x^(4)+8x'''+42x''+104x'+169x=0
特征根是x1=x2=-2+3i，x3=x4=-2-3i
通解该怎么写？看书没看明白

Answer 1

通解为e^(-2x)*(C1cos(3x)+C2sin(3x))

追问

四阶的

四阶的

追答

dsolve('D4y+8*D3y+42*D2y+104*Dy+169*y=0','x')
ans =
C1*exp(-2*x)*sin(3*x)+C2*exp(-2*x)*cos(3*x)+C3*exp(-2*x)*sin(3*x)*x+C4*exp(-2*x)*cos(3*x)*x

追问

谢谢

Answer 2

x=e^(-2t)*(c1t+c2)(c3cos3t+c4sin3t).

Answer 3

x = e^(-2t) [(C1+C2t)cos3t + (C3+C4t)sin3t]