Electronic Journal of Differential Equations, Vol. 2005(2005), No. 84, pp. 1-8. Title: Periodic solutions of polynomial non-autonomous differential equations Author: Mohamad A. M. Alwash (West Los Angeles College, CA, USA) Abstract: We present some results on the number of periodic solutions for scalar non-autonomous polynomial equations of degree five. We also consider a class of polynomial equations of any degree. Our results give upper bounds for the number of limit cycles of two-dimensional systems. Submitted July 7, 2005. Published July 25, 2005. Math Subject Classifications: 34C25, 34C07, 34C05. Key Words: Periodic solutions; polynomial non-autonomous equations; Abel differential equations; limit cycles; uniformly isochronous centers; Hilbert's sixteenth problem.