Well, for example, Maple has an in-depth step-by-step tutor for integration methods (making various different techniques available). These are aimed at teaching Mathematics to the student.
Why not something similar for ODEs ? ... If you take a look at the first two chapters of "Advanced Engineering Mathematics" by Kreyszig, you will see umpteen different techniques for solving First- and Second-Order ODEs. What I am wondering is why can't you have a tutor to solve ODEs making various different techniques available --- just like they have for integration methods ?
I can't see how Maple is teaching math when solving an ODE means shoving it into a black box called dsolve, and seeing what comes out.