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Re: DSolve difficulties ...

• To: mathgroup at smc.vnet.net
• Subject: [mg111894] Re: DSolve difficulties ...
• From: Slide <wdflannery at aol.com>
• Date: Tue, 17 Aug 2010 01:22:24 -0400 (EDT)
• References: <i4b1pu$b15$1@smc.vnet.net>

On Aug 16, 5:53 am, Themis Matsoukas <tmatsou... at me.com> wrote:
> In Mathematica "7.0 for Mac OS X x86 (64-bit) (November 11, 2008)", your equation,
>
> DSolve[y''[x] == 1/(y[x]*y[x]), y[x], x]
>
> has the solution
>
> Solve[(Log[-2 + 2 (C[1] + Sqrt[C[1]] Sqrt[C[1] - 2/y[x]]) y[x]]/C[1]^(
>     3/2) + (Sqrt[C[1] - 2/y[x]] y[x])/C[1])^2 == (x + C[2])^2, y[=
x]]
>
> which gives y implicitly as the solution of a mathematical equation.
>
> If you are getting inconsistent results over successive runs of mathematica, it is a good idea to quit the kernel and start a new session.
>
> Themis

Yes, starting anew solved that problem.

The question remains, can I get Mathematica to explain the steps it
took to arrive at the initial implicit solution?

And, if not, do you know where the derivation of the solution can be
found?