Re: Mathematica forgets a solution in DSolve!!!
- To: mathgroup at smc.vnet.net
- Subject: [mg78678] Re: [mg78648] Mathematica forgets a solution in DSolve!!!
- From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
- Date: Sat, 7 Jul 2007 05:51:13 -0400 (EDT)
- References: <200707060721.DAA20726@smc.vnet.net>
On 6 Jul 2007, at 16:21, Nope wrote:
> Hi, I just tried to solve a differential equation by writing down
> this code:
>
> DSolve[y'[x]^2 - y'[x]*x + y[x] == 0, y[x], x]
>
> Mathematica then tells me:
>
> {{y[x] -> x C[1] - C[1]^2}}
>
> but I noticed that y = x^2/4 is a solution too!!!
>
> Is it a Mathematica bug?
>
> Please answer me if you know something about this problem.
>
> Thanks :)
>
I seems to me that this involves a minor bug; which is Mathematica
somehow forgets to print a message about not being able to find all
the solutions. To see that, consider the more general equation:
eq = DSolve[Derivative[1][y][x]^2 + a*Derivative[1][y][x]*x + y[x]
== 0, y[x], x]
Solve::tdep:The equations appear to involve the variables to be
solved for in an essentially non-algebraic way. >>
Solve::tdep:The equations appear to involve the variables to be
solved for in an essentially non-algebraic way. >>
I have supressed the output, which is an algebraic equation
Mathematica is unable to Solve, but now if we substitute a -> -1 as
in yoru equation we will obtain:
eq /. a -> -1
Solve::ifun:Inverse functions are being used by Solve, so some
solutions may not be found; use Reduce for complete solution
information. >>
{{{y[x] -> (-(1/4))*E^(C[1]/2)*(2*x + E^(C[1]/2))}},
{{y[x] -> 2*(E^(C[1]/2)*x - 2*E^C[1])}}}
The second solution is exactly the solution you got (relace 2 E^(C[1]/
2) by C[1]).
Andrzej Kozlowski
- References:
- Mathematica forgets a solution in DSolve!!!
- From: Nope <bernardo.rimanno@email.it>
- Mathematica forgets a solution in DSolve!!!