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Having difficulty with "use Reduce for complete solution information"

I repeatedly get a response similar to the following:

In[13]:= Clear[Derivative]; gensol = 
 DSolve[y'[x] == (2 Sqrt[y[x]] - 2 y[x])/x, y[x], x]

During evaluation of In[13]:= Solve::ifun: Inverse functions are being used by Solve, so some solutions may not be found; use Reduce for complete solution information. >>

Out[13]= {{y[x] -> (E^(C[1]/2) + x)^2/x^2}}

How should I follow the instruction "use Reduce for complete solution information"? What command should I type it for complete solution information?

POSTED BY: David Arnold
5 Replies

Slight follow-up. If you search for

DSolve ifun

in the Documentation Center and look at the various Tutorial links that come up and then, in them search for the string ifun to find the warning messages in some of the examples, you will see some cases where such messages arise and some discussion of the circumstances that they are responding to. Here's an example

http://reference.wolfram.com/language/tutorial/DSolveClassificationOfDifferentialEquations.html

POSTED BY: David Reiss

Yes, I've read that URL. Thanks.

P.S. I added a little more to the problem via a new question.

http://community.wolfram.com/groups/-/m/t/398753?p_p_auth=skCcbI7K

POSTED BY: David Arnold
POSTED BY: David Reiss

This is a really great answer, extremely well explained, and much appreciated. But I still don't understand the phrase "use Reduce for complete solution information ."

What does this mean, "Use Reduce"? What command should I type in to follow this suggestion "Use Reduce"? In this situation, how do you use the command "Reduce"?

POSTED BY: David Arnold
POSTED BY: David Reiss
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