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MathGroup Archive 2004

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Re: DSolve change in v5 -- undocumented error message

  • To: mathgroup at smc.vnet.net
  • Subject: [mg46762] Re: DSolve change in v5 -- undocumented error message
  • From: bobhanlon at aol.com (Bob Hanlon)
  • Date: Sun, 7 Mar 2004 01:33:40 -0500 (EST)
  • References: <c298r9$56c$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

eqn=n'[t]==r*n[t]*(1-n[t]/k);

ans1 =DSolve[eqn,n[t],t][[1]];

Off[Solve::ifun];

ans2 = ans1 /. 
      Solve[(n[0] /. 
                (ans1 /. t->0))==n0, 
          C[1]][[1]] // Simplify

{n[t] -> (E^(r*t)*k*n0)/
    (k + (-1 + E^(r*t))*n0)}

ans2 /. t->0

{n[0] -> n0}

eqn /.Join[ans2, 
      D[ans2, t]//Simplify]//
  Simplify

True


Bob Hanlon

In article <c298r9$56c$1 at smc.vnet.net>, Gareth Russell <gjr2008 at columbia.edu>
wrote:

<< The following expression used to work in v4:

DSolve[{n'[t] == r*n[t]*(1 - n[t]/k), n[0] == n0}, n[t], t]

In v5, I get the message

"DSolve::bvfail: For some branches of the general solution, unable to 
solve the conditions."

Clicking on the "More" link takes me to a page in the Help Browser with 
"Notes for this message have not yet been added."

Interestingly, the expression without initial conditions works just 
like before

In[31]:=
DSolve[{n'[t] == r*n[t]*(1 - n[t]/k)}, n[t], t]

Out[31]=
\!\({{n[t] \[Rule] \(\[ExponentialE]\^\(r\ t + k\ C[1]\)\ k\)\/\(\(-1\) 
+ \
\[ExponentialE]\^\(r\ t + k\ C[1]\)\)}}\)

Does anyone know what is being done differently in v5. And more 
practically, is there a way to recover v4's ability to get a solution. 
Perhaps with assumptions?


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