Could you recommend some classic textbooks on ordinary/partial differential equation?

Solution 1:

Since you like the writing style of Courant and John... for PDEs there are of course F. John's Partial Differential Equations, and also Courant and Hilbert's Methods of Mathematical Physics.

Solution 2:

Good books on ODE would be:

1) Ordinary Differential Equations by Morris Tenenbaum and Harry Pollard

2) Differential Equations by George F. Simmons

3) Ordinary Differential Equations by E.Coddington

For PDE, I request you to take a look at this link: http://www.physicsforums.com/showthread.php?t=175382