Re: Mathematica forgets a solution in DSolve!!!
- To: mathgroup at smc.vnet.net
- Subject: [mg78688] Re: Mathematica forgets a solution in DSolve!!!
- From: dh <dh at metrohm.ch>
- Date: Sat, 7 Jul 2007 05:56:28 -0400 (EDT)
- References: <f6kqt1$kcb$1@smc.vnet.net>
Hi Nope,
what you got is termed a singular solution. At every point of this
solution there is a regular solution that is "tangent" to it. To see
what is going on do:
Plot[Evaluate[AppendTo[Table[c x-c^2,{c,0,6}],Sqrt[x]]],{x,0,10}]
This ODE is discussed (with yreplaced by -y) at:
http://en.wikipedia.org/wiki/Singular_solution
hope this helps, Daniel
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 :)
>