Books that explain differential equations in terms of complex variable theory?

[Simfish]

Hello,

so I know that complex variable theory is VERY relevant to the field of differential equations. The question is - are there any good not-extremely-abstruse books on differential equations that actually EXPLICITLY use complex variables?

Thanks!

[Chris Hillman]

Many topics in differential equations are best treated in the complex domain. Obvious examples include elliptic functions, hypergeometric equations, Painleve transcendents, and differential Galois theory. Try:

Jones and Singerman, Complex Functions, Cambridge University Press.

Harold T. Davis, Introduction to Nonlinear Differential Equations and Integral Equations, Dover.

Here are two odd ducks!:

Anonymous, Advanced Methods for Solving Differential Equations, REA, 1982. (Might be hard to obtain.)

Michio Kuga, Galois's Dream, Birkhauser.

[AiRAVATA]

INCE, E.L Ordinary Differential Equations, Dover.