DSolve for y'[x] == (x^2 + xy[x] + 4 y[x]^2)/x^2

Questions
,
1

I downloaded a student trial of the latest version of Mathematica and am hung up on its differential equation solver. I enter:

DSolve[y'[x] == (x^2 + xy[x] + 4 y[x]^2)/x^2, y[x], x]

…and receive as output an echo of my input. Dsolve processes other differenial equations fine in my environment, including the reference examples. What’s going on here?

2

I think your second term is missing a space x y not xy for multiplying x and y you need a space inbetween

DSolve[y'[x] == (x^2 + x y[x] + 4 y[x]^2)/x^2, y[x], x]

gives

{{y[x] -> 1/2 x Tan[2 (C[1] + Log[x])]}}
3

Oh, of course, it’s always the little details. Thank you.

4

The following code also produces an echo, and I can’t parse out why:

DSolve[{y'[x] == (x^2 + x y[x] + 4 y[x]^2)/x^2, y[1] == 1}, y[x], x]
5

Make sure you always put:

ClearAll["Global`*"]

at the beginning of your notebook

6

Which Mathematica version on which OS?
Works for me with 8.0.4 or 9.0.1 on MacOS 10.8.5.

In[1]:= $Version                                                                        
Out[1]= 9.0 for Mac OS X x86 (64-bit) (January 24, 2013)

In[2]:= DSolve[{y'[x] == (x^2 + x y[x] + 4 y[x]^2)/x^2, y[1] == 1}, y[x], x]            

Solve::ifun: Inverse functions are being used by Solve, so some solutions may not be
     found; use Reduce for complete solution information.

                           ArcTan[2]
                  x Tan[2 (--------- + Log[x])]
                               2
Out[2]= {{y[x] -> -----------------------------}}
                                2

In case a non-printing character slipped in, try copying it as plain text (Edit menu - CopyAs) and
pasting it into a new notebook window.

7

Would anyone be able to take a few moments and ask someone who knows how to interpret

Solve::ifun: Inverse functions are being used by Solve, so some solutions may not be
      found; use Reduce for complete solution information

to explain how to do what this directs us to do?

The help page for DSolve shows no example using Reduce, but it does have one example under “Possible Issues” which gives this message.

Replacing DSolve with Reduce doesn’t seem to do this. There don’t appear to be any documented option for DSolve to instruct it to use Reduce instead of Solve.

I’m wondering if there might be a whole new level of DSolve that doesn’t seem to be documented, and if so would it be possible to get this incorporated into the help page.