微分方程组(dX)/(dt)=AX+e~(αt) sum from k=0 to m(B_kt~k)特解结构定理及应用

对于常系数非齐线性微分方程组(dX)/(dt)=AX+F(t),当强迫项F(t)=e~(at) sum from k=0 to m(B_kt~k)(这里Bk=(b1k,b2k,…,bnk)T∈Rn),给出了微分方程组(dt)/(dX)=AX+F(t)特解(t)的结构定理和计算方法,使求特解-X(t)的积分运算转化为简单的代数运算.解决了计算机特解(t)的计算问题.

Structure Theorem of the Special Solution of the System of Differential Equations (dX)/(dt)=AX+e~(αt) sum from k=0 to m(B_kt~kBktk) and Its Application

For the system of linear inhomogeneous differential equations with constant coefficient (dX)/(dt)=AX+F(t),we give the structure theorem and the calculating method of its special solution when the forcing item F(t)=e~(αt) sum from k=0 to m(B_kt~k) (in which Bk=(b1k,b2k,…,bnk)T∈Rn).We turn the integral operation of seeking the special solution (t) into the algebraic operation and solve the calculating problem of seeking special solution by computer.