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MathGroup Archive 2005

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Re: DSolve and K$31, i am puzzled

  • To: mathgroup at smc.vnet.net
  • Subject: [mg57081] Re: [mg57078] DSolve and K$31, i am puzzled
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Sun, 15 May 2005 03:03:34 -0400 (EDT)
  • Reply-to: hanlonr at cox.net
  • Sender: owner-wri-mathgroup at wolfram.com

K$31 is an internal local variable that did not get get resolved.  These should 
not show up.  This does not occur with the Mathematica version that I have

$Version

5.1 for Mac OS X (January 27, 2005)

The form of the output is simpler if you provide a boundary condition such as 
f[0]==f0

soln = DSolve[{
          f'[t]==Sign[p2*Exp[F2*t]-p1*Exp[F1*t]+p],
          f[0]==f0},f[t],t]//Flatten//Simplify

{f[t] -> (f0*(p - E^(F1*t)*p1 + 
       E^(F2*t)*p2) + 
     Sqrt[(p - E^(F1*t)*p1 + E^(F2*t)*p2)^
        2]*t)/(p - E^(F1*t)*p1 + 
     E^(F2*t)*p2)}

Simplify[soln,
  Element[{p,p1,p2,F1,F2,t}, Reals]]

{f[t] -> Piecewise[
    {{f0 - t, E^(F1*t)*p1 > 
       p + E^(F2*t)*p2}}, f0 + t]}


Bob Hanlon

> 
> From: David Boily <dsboily at fastmail.ca>
To: mathgroup at smc.vnet.net
> Date: 2005/05/14 Sat AM 04:58:23 EDT
> Subject: [mg57081] [mg57078] DSolve and K$31, i am puzzled
> 
> When i try to solve this differential equation with the command:
> 
> In[1]:= DSolve[f'[t] == Sign[p2 Exp[F2 t] - p1 Exp[F1 t] + p], f[t], t]
> 
> where p, p1, p2, F1 and F2 are constants i get the answer
> 
>                         F1 t       F2 t
>                   (p - E     p1 + E     p2) (-K$31 + t)
> Out[1]= {{f[t] -> ------------------------------------- + C[1]}}
>                                F1 t       F2 t    2
>                     Sqrt[(p - E     p1 + E     p2) ]
> 
> what the hell is K$31? I have tried to find out with google or
> the mathematica 5 online docs but have found nothing.
> 
> can someone enlighten me?
> 
> David Boily
> Centre for Intelligent Machines
> McGill University
> Montreal, Quebec
> 
> 


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