Recommendations for textbooks on ordinary differential equations (ODEs) include I.V. Smirnov's "Higher Mathematics" volumes I and II, which provide a solid foundation without being overly complex. Daniel suggests "Elementary Differential Equations and Boundary Value Problems" by Boyce and DiPrima, while another popular choice is "Differential Equations" by Blanchard, Devaney, and Hall. Additionally, Rea's differential equations problem solver is noted as a valuable resource, and the Dover publication by Tenenbaum and Pollard is highlighted for its affordability. Arnold's work is also mentioned as a top recommendation in the field.