Owl: You can't always solve a DE with a neat formula. Euler's method says: stand at a point, read the slope the field demands, take a short straight hop of width Δx, land, repeat.
Each hop is exact for a linear path — but the true solution may curve, so error accumulates. Smaller steps usually help; they are not optional magic that you can skip forever.
Follow the arrows in short straight hops — where do you end up?
We'll try one careful step, then a tiny table, and talk honestly about step-size error.