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Re: DSolve and K$31, i am puzzled


David Boily wrote:
> 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

Those are "module variables" and the numbers give them unique names. 
They're needed because often the output from DSolve contains an 
unevaluated integral. Example:

In[1]:= DSolve[y'[x]==f[x], y,x]
Out[1]= {{y -> Function[{x}, C[1] + Integrate[f[K$371], {K$371, 1, x}]]}}

The K$371 variable is a dummy variable of integration and does not
affect the calculations.  Just replaced it by another symbol:

In[2]:= %/.{K$44 -> t}
Out[2]= {{y -> Function[{x}, C[1] + Integrate[f[t], {t, 1, x}]]}}

--
Igor Antonio
Wolfram Research, Inc.
www.wolfram.com

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