What would be a good introductory book for ODEs and PDEs with good concepts?

Question

I have reasonable undergraduate and graduate background(just ode & pde part is horrible).I want an introductory book that doesn't just list some ways to solve a bunch of equation.I want it to give me ideas necessary to make the ways feel reasonable and also keep things rigorous.I have no problem using different books for rigor and ideas.Also,a book of geometric flavor or connecting geometry to it would be very good.As, geometry is the main reason I am studying it.Thank You.

edit:it's not duplicate.I think I asked for something more than the answer's there provided.

Answer 1

For more conceptual/geometric perspectives on PDE's, that deviate somewhat from the common analysis views, there are

• Arnold, Lectures on partial differential equations
• Krasilshchik, Vinogradov et al., Symmetries and Conservation Laws for Differential Equations of Mathematical Physics
• Bryant, Chern et al., Exterior Differential Systems

Answer 2

You can try the following references:

$(1)\quad $ "Differential Equations" by Shepley L. Ross

$(2)\quad $ "Differential Equations with Applications and Historical Notes " by George Simmons

$(3)\quad $ "Differential Equations: Theory, Technique, and Practice" by George F. Simmons and Steven G. Krantz

$(4)\quad $ "Elements of partial differential equations" by Ian Sneddon

Besides for theory with solution (Practices purpose) you can also follow

$(5)\quad $ "Ordinary and Partial Differential Equations", and "Advanced Differential Equations" by M. D. Raisinghania

$(6)\quad $ "Differential Equations" by J. G. Chakravorty and P. R. Ghosh

$(7)\quad $ "An Introduction to Differential Equations" by Ram Krishna Ghosh and Kantish Chandra Maity

$(8)\quad $ "Differential Equations" by Richard Bronson