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Re: DSolve difficulties ...

  • To: mathgroup at smc.vnet.net
  • Subject: [mg111875] Re: DSolve difficulties ...
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Mon, 16 Aug 2010 05:55:49 -0400 (EDT)

You can plot the solution of the implicit equation

eqn = DSolve[
     y''[x] == 1/(y[x]*y[x]), y[x], x][[1]] /.
   {C[1] -> c1, 
    C[2] -> c2, y[x] -> y} //
  FullSimplify

(Sqrt[c1]*y*Sqrt[c1 - 2/y] + 
     Log[2*y*(Sqrt[c1]*Sqrt[c1 - 2/y] + c1) - 2])^2/
     c1^3 == (c2 + x)^2

Reduce[Cases[eqn, Log[expr_] :> expr,
    Infinity][[1]] > 0, y, Reals]

c1 > 0 && y >= 2/c1

Manipulate[Column[{
   eq = (Sqrt[c1]*y*Sqrt[c1 - 2/y] + 
         Log[2*y*(Sqrt[c1]*Sqrt[c1 - 2/y] + c1) - 2])^2/
      c1^3 == (c2 + x)^2,
   ContourPlot[
    Evaluate[eq],
    {x, -4, 4}, {y, 2/c1, 4},
    PlotRange -> {{-4, 4}, {.35, 4}},
    ImageSize -> 400]}],
 {{c1, 1}, .75, 5, .05, Appearance -> "Labeled"},
 {{c2, 0}, -5, 5, .1, Appearance -> "Labeled"}]


Bob Hanlon

---- Helen Read <hpr at together.net> wrote: 

=============
On 8/14/2010 6:33 AM, Slide wrote:
> Yesterday I typed in the following command line, into the student
> version of Mathmatica .
>
> DSolve[y''[x] == 1/(y[x]*y[x]), y[x], x]
>
> and got a complicated Solve command and expression back with the
> comment 'The equations appear to involve the variables to be solved
> for in an essentially non-algebraic way.'

I get a perfectly good solution.

> OK, that was yesterday, fortunately I didn't close the session.
>
> However, now when I try the same command, I get a null response.

Try it in a fresh session. Remember that Mathematica remembers 
everything you do in a session, and you might have done something that 
defined x or y or y[x] in some way.


-- 
Helen Read
University of Vermont


--

Bob Hanlon



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