Exact solutions of a linear functional differential equation (Q2723218)

Here, the author presents a summary of some of the results in his book [On the accurate distribution of characteristic roots and stability of linear delay differential systems] for the use of readers who are not familiar with the Chinese language. The results concerning solutions to NEWLINE\[NEWLINEx'(t)+ax(t)+ bx (t-\tau)= 0,\tag{*}NEWLINE\]NEWLINE where \(a,b,\tau\) are constants and \(\tau>0\), through its characteristic equation NEWLINE\[NEWLINE\lambda+ a+be^{-\tau \lambda}=0NEWLINE\]NEWLINE are discussed. The fundamental solution to (*) is given.