Which Euler Method Was It Again?

The eternal struggle of math students everywhere! Batman Beyond (aka "Euler's Method") confidently shows up to solve differential equations, but our glowing skeleton villain is completely lost. "Do you have the slightest idea how little that narrows it down?" is basically every student trying to remember which numerical approximation technique to use on their calculus exam. There are like 50 different Euler methods—explicit, implicit, modified, improved, backward... The professor might as well have said "use math" as a hint. The panic is real when you're staring at that blank exam paper trying to remember if it's the one with the tangent lines or the one with the fancy error terms!