Good day Brian,
> The documentation for solving equations says that SOLVERADCAN allows
> more equations with exponentials and logarithms to be solved.
>
> SOLVERADCAN:TRUE;
> SOLVE(log(a*x)=C*log(b*x),x);
>
> does the trick.
Yes, it does, thank you! It is unfortunate that it does nothing to help
solve(exp(a*x)=C*exp(b*x),x);. You did, however, improve my confidence
in the tool (I'm not convinced just yet though).
> >
> > (C1) SCSIMP(a*(sin(x))^2 +a*(cos(x))^2 );
> > 2 2
> >(D1) a SIN (x) + a COS (x)
>
> Reading the section on Trigonometric functions says to use TRIGSIMP
> for simplifying trigonometric expressions.
>
> TRIGSIMP(a*sin(x)^2+a*cos(x)^2);
>
> will work.
Does it? Really? It does nothing here...
[lemire@romeo lemire]$ maxima
GCL (GNU Common Lisp) Version(2.4.0) Wed May 9 12:02:00 CDT 2001
Licensed under GNU Library General Public License
Contains Enhancements by W. Schelter
Maxima 5.6 Wed May 9 12:01:49 CDT 2001 (with enhancements by W. Schelter).
Licensed under the GNU Public License (see file COPYING)
(C1) TRIGSIMP
:true;
(D1) TRUE
(C2) SCSIMP(a*(sin(x))^2+a*(cos(x))^2);
2 2
(D2) a SIN (x) + a COS (x)
(C3) TRIGSIMP:true;
(D3) TRUE
(C4) SCSIMP(a*(sin(x))^2+a*(cos(x))^2);
2 2
(D4) a SIN (x) + a COS (x)
(C5)
(What happened on the first line...? well, that's the crappy user
interface, but I won't complain... I can live with that. Beside, people
can write front-ends to it.)
>>From reading the description of SOLVE I decided to give it a helping
> hand by dividing by EXP(b*x),
>
> q:EXP(a*x)=C*EXP(b*x);
> SOLVE(q/EXP(b*x),x);
which amounts to...
(C1) solve(exp(a*x-b*x)=C,x);
LOG(C)
(D1) [x = - ------]
b - a
Yes, fine, it works if you simplify the equation yourself first. There
was another idea in the same direction before. Basically, if Maxima
doesn't work, you just rewrite your equation in various ways until it
does solve it. I'd rather have a better answer if you have one. That's
just not very convincing.
These two problems : EXP(a*x)=C*EXP(b*x)
and a*(sin(x))^2+a*(cos(x))^2 are still two relatively easy problem
that make maxima choke as far as I can tell. (Please, prove me wrong!)
--
Daniel Lemire, Ph.D.
http://www.ondelette.com/