How to define "D"prefix operator



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> Please tell me how to define "D"prefix  operator.D means prefix operator
> and "d/dx" differential operator.I want to solve "(D+x) (D+2*x) exp(x)".
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While it is probably possible to do all that is necessary in Maxima
it is likely not worth your doing it, or finding/reading one of the
several papers on introducing operators in Macsyma.
http://dl.acm.org/citation.cfm?id=32488
and others,  by Golden and Grossman

As I recall you need to worry about a bunch of things you may have not
noticed.  Like the number 3 is also an operator which when applied to Z
returns 3,  or maybe 3*Z?

My suggestion is you deal with D (etc) operators as elements in a
(non-commuting) ring and do polynomial arihmetic,
and then write a program that applies this to an
expression according to how you want to interpret stuff.

Or just decide not to use operator expressions; they save some
handwriting, but I suspect that in particular cases they don't buy you
much when a computer is doing the algebra.