cost 0 0 sint「 cost sint g(A=col+CA f(a=e 0 cost -sint 0 int cost cost roosters in x(t)=eAx(O)= sint r sint cost52rcost-rsint x,(t) 一阶线性非齐次常系数常微分方程组 dt=a,x,(t)+a, x, (t) +a,x t)+b t) dt2 *g (t)+a,x, (t)+.+a2*, (t)+b, (t) =anx(t)+anx, (t)+ .+a,(t)+b, (t) 令x(t)=x(t),x2t),…,xn(t) b(t)=[b,,t2t),…,bn(t) 12 a 方程组化为矩阵方程 Ax+b 采用常数变易法求解之;齐次方程的解为ec,可设非齐次方程的解为 代入方程,得 dx d L (e )c(t) Ax(址)+e dt =Ax(t)+b(t) tb(t) dt                  0 1 cost 0 0 sint cost sint tA g(A)= c I+ c A = + = = f(A)= e 0 cost -sint 0 -sint cost                        1 1 2 1 2 2 1 2 cost sint r rcost +rsint x(t) tA x(t)= e x(0)= = = -sint cost r rcost -rsint x (t) 三、 一阶线性非齐次常系数常微分方程组           1 11 1 12 2 1n n 1 2 21 1 22 2 2n n 2 n n1 1 n2 2 nn n n dx = a x(t)+ a x (t)+ + a x (t)+ b(t) dt dx = a x(t)+ a x (t)+ + a x (t)+ b (t) dt dx = a x(t)+ a x (t)+ + a x (t)+ b (t) dt 令 方程组化为矩阵方程 dx = Ax + b dt 采用常数变易法求解之；齐次方程的解为 tA e c ，可设非齐次方程的解为 tA e c(t)， 代入方程，得： dx d dc dc tA tA tA = (e )c(t)+ e = Ax(t)+ e = Ax(t)+ b(t) dt dt dt dt dc -tA = e b(t) dt             T 1 2 n T 1 2 n 11 12 1n 21 22 2n n1 n2 nn x(t)=[x (t),x (t), ,x (t)] b(t)=[b (t),b (t), ,b (t)] a a a a a a a a a