Dear Gary,
there is a lot of notation in Mathematica which might be unfamiliar at first but is very powerful. Most of the symbols are really useful.
If you type
? /.
so a question mark in front of the symbol you don't know you get a lot of info on it. If you then click on the >> symbol you go to the help page. You can also do this by highlighting the symbol and then clicking, e.g. Fn+F1 on a Mac, and something similar on Windows.
/.
means "replace all". The help page shows how to use it and lots of examples. The examples are interactive so you can try out what the command does. These pages are really useful.
In the example above (last post)
y'[x] + x y''[x] == y[x]/x /. {y'[x] -> -2 - y[x]/x}
you can read the /. symbol as "such that". So use the equation such that the replacement rules are taken into consideration. So it basically just substitutes y'[x] by -2-y[x]/x.
It is quite important to learn the (few and logical) rules behind the Wolfram Language. You will see in this community that you can do an awful lot of cool stuff with it. The linguistic input and Wolfram Alpha are very useful, but it is also important to learn the syntax behind the language. There are excellent tutorials on the Wolfram Website as well:
http://www.wolfram.com/training/courses/
Lot's of them are on demand and free! I understand though that the step-by-step solution is a very nice feature and that you want to use that for as many problems as possible.
Hope this helps,
Marco