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Re: DSolve difficulties ...

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  • Subject: [mg111874] Re: DSolve difficulties ...
  • From: Slide <wdflannery at>
  • Date: Mon, 16 Aug 2010 05:55:33 -0400 (EDT)
  • References: <i45rdj$g3o$> <i48jgi$e46$>

On Aug 15, 7:36 am, Helen Read <h... at> 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[1]^(3/2)))
>      Log[-2 + 2 (C[1] + Sqrt[C[1]] Sqrt[C[1] - 2/y[x]]) y[x]] + (
>      Sqrt[C[1] - 2/y[x]] y[x])/C[1])^2 == (x + C[2])^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.)
> --
> Helen Read
> 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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