Suppose that a hypothetical math grad student was pretty comfortable with first-year real variables and algebra, and had even studied some other things (algebraic geometry, Riemannian geometry, complex analysis, algebraic topology, algebraic number theory), but had miraculously never taken a differential equations course (despite the geometry) and wanted to learn some ODEs. What book would you recommend? This student would be happy to learn more analysis if necessary to understand what's in this ODE book.

In other words: I'm asking for your recommendations for a ODE book that is allowed to have arbitrary prerequisites from analysis and algebra and topology and even geometry, but with no knowledge of differential equations presumed.

Thank you!

(Note: It could have occurred to the hypothetical student to talk to his/her advisor/other faculty members, but in that case the student would still be interested in MathOverflow's response.)

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