Electronic Journal of Differential Equations, Vol. 2024 (2024), No. 54, pp. 1-22. Title: Solving linear differential equations with mixed arguments Author: George L. Karakostas (Univ. of Ioannina, Greece) Abstract: We find expressions for solutions to an initial value problem of a linear n-dimensional differential equation. This equation has time deviations of mixed type (advanced and delayed) that have fixed points. The key assumption is that these deviations are odd functions. Submitted May 16, 2024. Published September 17, 2024. Math Subject Classifications: 34K06, 34K99. Key Words: Differential equations with mixed arguments; nonsingular matrices.