Re: Mathematica forgets a solution in DSolve!!!
- To: mathgroup at smc.vnet.net
- Subject: [mg78703] Re: Mathematica forgets a solution in DSolve!!!
- From: Bill Rowe <readnewsciv at sbcglobal.net>
- Date: Sat, 7 Jul 2007 06:04:14 -0400 (EDT)
On 7/6/07 at 3:21 AM, bernardo.rimanno at email.it (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?
Probably not. I think the answer can be found in the
documentation for DSolve. Specificaly,
DSolve can find general solutions for linear and weakly
nonlinear partial differential equations. Truly nonlinear
partial differential equations usually admit no general solutions.
To me this implies DSolve will not find all solutions to such
problems. And your problem is clearly nonlinear with respect to
the derivative.
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