Re: DSolve difficulties ...

• To: mathgroup at smc.vnet.net
• Subject: [mg111843] Re: DSolve difficulties ...
• From: Helen Read <hpr at together.net>
• Date: Sun, 15 Aug 2010 07:36:46 -0400 (EDT)
• References: <i45rdj\$g3o\$1@smc.vnet.net>

```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.'

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.)

--
University of Vermont

```

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