ODE introduction textbook
I think these two are quite good:
Elementary Differential Equations with Boundary Value Problems (Edwards &Penney)
An Introduction to the Theory of Numbers (G Hardy)
For learning ODE's, a popular undergraduate book is
1.)Differential Equations with Boundary Value problems-Polking, Bogges, Arnold.
If you want to see many examples, I recommend you get the
2.)Schaum's Outline on Differential equations-Bronson,Costa.
From personal experience I highly recommend both of these books. If you want to see slightly more advance topics with a geometric taste I recommend
3.) Ordinary Differential Equations-V.I. Arnold
As for Number theory, if you want a computational approach, consider
1.) Elementary Number Theory-Burton
For a more theoretical approach,
2.) A classical Introduction to Modern Number theory-Rosen, Ireland 3.) Introduction to Analytic Number Theory-Apostol