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This is an amazing book. Arnold's style is unique - very intuitive and geometric. This book can be read by non-mathematicians but to really appreciate its beauty, and to understand the proofs that sometimes are just sketched, it takes some mathematical culture. This is the way ordinary differential equations should be taught (but they are not).
Ordinary Differential Equations by Edward L. Ince Summary
Among the topics covered in this classic treatment are linear differential equations; solution in an infinite form; solution by definite integrals; algebraic theory; Sturmian theory and its later developments; much more. 'Highly recommended' — Electronics Industries.