Simplifying ODE solutions by introducing arbitrary constants

Hi,
if you already know this and it does not answer your question I 
apologize (I have not looked at the thread you refer), but just in case, 
have you tried using atvalue?:

(%i2) atvalue(f(x),x=0,%c1)$
(%i3) atvalue('diff(f(x),x,1),x=0,%c2)$
(%i4) atvalue('diff(f(x),x,2),x=0,%c3)$
(%i5) desolve('diff(f(x),x,3)-2*'diff(f(x),x,2)+'diff(f(x),x)=0, f(x));
(%o5) f(x) = %c3*x*%e^x-%c2*x*%e^x+(2*%c2-%c3)*%e^x+%c3-2*%c2+%c1

Regards,
Jaime

On 23-10-2013 13:57, Robert Pollak wrote:
> Hello list,
>
> referring to ODE solutions like
>
> (%i1) desolve('diff(f(x),x,3)-2*'diff(f(x),x,2)+'diff(f(x),x)=0, f(x));
> (%o1)
> f(x)=x*%e^x*(at('diff(f(x),x,2),x=0))+at('diff(f(x),x,2),x=0)+%e^x*(2*(at('diff(f(x),x,1),x=0))-at('diff(f(x),x,2),x=0))-x*%e^x*(at('diff(f(x),x,1),x=0))-2*(at('diff(f(x),x,1),x=0))+f(0)
>
> , Dan Stanger unsuccessfully asked this list in 2006 [1]:
>> Does anyone know a convenient way of converting from the form
>> returned from desolve, to the form involving arbitrary constants?
>
> For my teaching, I would now need the same: some way to replace all the
> 'at' terms by constants %c1 to %cn to get a form like
>
> f(x)=%c1+%c2*%e^x+%c3*x*%e^x
>
> . I don't want to raise any expectations, but: If someone wrote a Maxima
> patch (presumably to src/desoln.lisp [2]) to get this functionality,
> would it be ok to offer it via a keyword (e.g. 'mergeconst') as optional
> 'desolve' parameter?
>
>
> Best regards,
> Robert Pollak
>
>
> [1] http://article.gmane.org/gmane.comp.mathematics.maxima.general/10092
> [2] Btw., what are the files share/diffequations/desoln.[mac,usg] good for?
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