Simplifying ODE solutions by introducing arbitrary constants
Subject: Simplifying ODE solutions by introducing arbitrary constants
From: Robert Pollak
Date: Wed, 23 Oct 2013 14:57:45 +0200
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?