Mathematica, WolframAlpha, and Grapher provide tools for solving differential equations. But you don't get to see what's happening under the hood. Differential equations often don't have a tidy closed form solution, and a numerical method is needed. Euler's method requires only a differential equation (not necessarily separable), and an initial value.
That said, there are a few steps in using Euler's method, and after spending a couple of days on it in class, I decided it might be helpful to have a graphical organizer. I came up with this (also available as pdf):
This screencast shows how it can be used.