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 > >