Subject: Solving a single equation of two variables
From: Dan Stanger
Date: Tue, 16 Sep 2003 13:08:35 -0400
Herbert_Desson@jltgroup.com wrote:
> I was using it as a test case to increase my understanding of Maxima. After
> receiving your replies I looked at intermediate stages of the equation and
> found it interesting how quickly Maxima breaks down in giving useful results
> for non-polynomial equations.
It is unreasonable to disparage Maxima for not finding a closed form solution,
if one doesn't exist. The commercial Macsyma finds the solution for x=log(r)+r,
as [r = lambert_w(%e^x)], btw.
Most of the problems that come up dont have closed form solutions, the power
of symbolic methods allow one to determine approximations also, easily
in those cases.
If you exponentiate both sides, using the trig substitution I suggested you
could
expand terms such as exp(cos(theta)) in a infinite series involving bessel
functions,
You could also try to compute a fourier series for the inverse function defined
by
the equation, using a symbolic tool.
It depends what you are trying to achieve.