Re: Mathematica forgets a solution in DSolve!!!
- To: mathgroup at smc.vnet.net
- Subject: [mg78770] Re: [mg78648] Mathematica forgets a solution in DSolve!!!
- From: Devendra Kapadia <dkapadia at wolfram.com>
- Date: Mon, 9 Jul 2007 01:35:17 -0400 (EDT)
- References: <200707060721.DAA20726@smc.vnet.net>
On Fri, 6 Jul 2007, 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 :)
>
Hello,
Thank you for the above example where DSolve fails to return the
particular solution y = x^2/4 for the equation.
A workaround for finding this singular solution is to construct the
envelope of the one-parameter family of straight lines represented
by the general solution, as follows:
==========================
In[1]:= $Version
Out[1]= 6.0 for Linux x86 (32-bit) (April 29, 2007)
In[2]:= (sol = DSolve[y'[x]^2 - y'[x]*x + y[x] == 0, y, x])//InputForm
Out[2]//InputForm= {{y -> Function[{x}, x*C[1] - C[1]^2]}}
In[3]:= z[x_]= y[x]-(y[x]/.sol[[1]]);
In[4]:= Solve[{z[x]==0, D[z[x], C[1]]==0}, y[x], C[1]]//InputForm
Out[4]//InputForm= {{y[x] -> x^2/4}}
=========================
At present, DSolve returns the general solution for examples such
as the one considered by you. We plan to add the functionality for
returning singular solutions of nonlinear ordinary differential equations
(perhaps using an option) in a future version of Mathematica.
I apologize for the confusion caused by this limitation.
Sincerely,
Devendra Kapadia,
Wolfram Research, Inc.
- References:
- Mathematica forgets a solution in DSolve!!!
- From: Nope <bernardo.rimanno@email.it>
- Mathematica forgets a solution in DSolve!!!