Hi Gary,
this probably does not really answer your question. I am also not quite sure what your input was and I cannot reproduce what you get, but if you do the calculation in two steps it works. First you take the first derivative
then calculate another derivative of the first result.
As you see you get to see step-by-step solutions. The second solution contains the first and second derivative. You then need to substitute the first result:
y'[x] + x y''[x] == y[x]/x /. {y'[x] -> -2 - y[x]/x}
The only thing that remains is to solve for y''[x].
Solve[%, y''[x]]
From you screenshot I see that you have Mathematica and not only Wolfram Alpha, so this recipe should work. You have to do a bit of work by hand, but you get to see all the other intermediate steps shown.
I am not sure how to get this with step-by-step solutions with one query to Wolfram Alpha. What was your input?
Cheers,
M.