I'm not sure how well it would fit as a first course, but the thing that really helped me understand what's behind differential equations is Steven Strogatz's w

I'm not sure how well it would fit as a first course, but the thing that really helped me understand what's behind differential equations is Steven Strogatz's wonderful book "Nonlinear Dynamics And Chaos"[0]. [0] https://www.amazon.com/gp/aw/d/0813349109/ https://www.amazon.com/gp/aw/d/0813349109/