Solutions of the neutral differential-difference equation \(\alpha{}x'(t) + \beta{}x'(t-r) + \gamma{}x(t) + \delta{}x(t-r) = f(t)\) (Q1205619)

The author studies the particular solutions and complementary functions for the neutral differential-difference equation \(\alpha x'(t)+\beta x'(t-r)+\gamma x(t)+\delta x(t-r)=f(t)\), where \(\alpha,\beta,\gamma,\delta\in\mathbb{R}\) with \(\alpha,\beta\neq 0\). The solutions defined on the whole real axis are obtained in the forms of a convolution type integral and of infinite series.