       Re: DSolve difficulties ...

• To: mathgroup at smc.vnet.net
• Subject: [mg111874] Re: DSolve difficulties ...
• From: Slide <wdflannery at aol.com>
• Date: Mon, 16 Aug 2010 05:55:33 -0400 (EDT)
• References: <i45rdj\$g3o\$1@smc.vnet.net> <i48jgi\$e46\$1@smc.vnet.net>

```On Aug 15, 7:36 am, Helen Read <h... 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.'
>
> Adding to my previous post:
>
> OK, the solution to DSolve comes out like this:
>
> Solve[((1/(C^(3/2)))
>      Log[-2 + 2 (C + Sqrt[C] Sqrt[C - 2/y[x]]) y[x]] + (
>      Sqrt[C - 2/y[x]] y[x])/C)^2 == (x + C)^2, y[x]]
>
> That is, Mathematica is able to solve the differential equation, but the
> solution is given implicitly, rather than solved for y[x]. It got to the
> part where it wants to solve for y[x] in terms of x, can't do it, and
> quits there.
>
> If you then evaluate the output (the Solve[ ] ), you will get the
> message about "essentially non-algebraic" which is Mathematica's way of
> saying it cannot solve the equation explicitly. (It would have to begin
> with, if it could.)
>
> --
> University of Vermont

Hi Helen,

Thanks for your response.  Yep, that's what I got for a solution.  Is
it possible for me to get Mathematica to explain, or at least list,
the steps it used to arrive at that solution?  Note that had I
remembered to put a minus constant in front of the right side of the
differential equation, it would be the world's first, that is, the
differential equation for a falling object acted on by gravity in one
dimension ! ...... Newton's first DE, and it's a bear !

```

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