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Re: Problem with DSolve

  • To: mathgroup at smc.vnet.net
  • Subject: [mg96498] Re: Problem with DSolve
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Sat, 14 Feb 2009 04:14:44 -0500 (EST)
  • Organization: The Open University, Milton Keynes, UK
  • References: <gn3bnf$pt9$1@smc.vnet.net>

In article <gn3bnf$pt9$1 at smc.vnet.net>, Tony <aezajac at optonline.net> 
wrote:

> can anyone help what is wrong?
> On version 7 I enter
> 
>    DSolve[{y'[x]==.02*y[x]-y[x]^2,y[0]==a},y[x],x]
> 
> and get
> 
>        During evaluation of In[58]:= Solve::ifun: Inverse functions are being 
>        used by Solve, so some solutions may not be  found; use Reduce for 
>        complete solution information. >>
>        During evaluation of In[58]:= Solve::ifun: Inverse functions are being 
>        used by Solve, so some solutions may not be found; use Reduce for 
>        complete solution information. >>
>        During evaluation of In[58]:= DSolve::bvnul: For some branches of the 
>        general solution, the given boundary conditions lead to an empty 
>        solution. >>

As a rule of thumb, one should always use exact numbers whenever 
possible when looking for *symbolic* solutions to an equation. Also, it 
is a good practice to request the solution as a pure function for it is 
easier afterwards to check the validity of the solution. Having done 
that, Mathematica 7.0 (and 6.0.3 alike) only returns a particular 
solution.

In[1]:= DSolve[{y'[x] == 2/100*y[x] - y[x]^2, y[0] == a}, y, x]
y'[x] == 2/100*y[x] - y[x]^2 /. %[[1]]
{$Version, $ReleaseNumber}

During evaluation of In[1]:= Solve::ifun: Inverse functions are being 
used by Solve, so some solutions may not be found; use Reduce for 
complete solution information. >>

Out[1]= {{y -> Function[{x}, (a E^(x/50))/(1 - 50 a + 50 a E^(x/50))]}}

Out[2]= True

Out[3]= {"7.0 for Microsoft Windows (32-bit) (November 10, 2008)", 0}

Regards,
--Jean-Marc


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