       Is a solution possible to this exponential equation?

• To: mathgroup at smc.vnet.net
• Subject: [mg6994] Is a solution possible to this exponential equation?
• From: Michael Hucka <hucka at eecs.umich.edu>
• Date: Thu, 1 May 1997 14:48:40 -0400 (EDT)
• Organization: University of Michigan EECS, Ann Arbor, Mich., USA
• Sender: owner-wri-mathgroup at wolfram.com

```I have a pair of equations involving exponentials that I'd like to be able to
solve for one of the variables, but I can't seem to find a way to do it.  MMA
3.0's Solve operator complains its usual complaint about the equation
involving transcendental functions.  Quite possibly there is no analytical
solution, but I'd like to find out from the experts out there about what
approaches one might try.  The equations are as follows:

1/2 = kc * Exp[ -a * w^2 * x^2 ]  -  ks * Exp[ -a * b^2 * w^2 * x^2]

where a and b are constants, and kc, ks, w and x are variables.  There is an

kc - ks = Sqrt[ 1/2 ]

So there are 2 equations and 4 unknowns.  I'd like to solve this for w, or
rather, to express w in terms of the other unknowns.  The problem, of course,
is that w is in the exponent of two of the terms.

What is the right approach to take in cases like this?  This is actually
something I've come across before in my work, but haven't had much luck with.

--
Mike Hucka    hucka at umich.edu    http://www.eecs.umich.edu/~hucka    University
PhD to be, computational models of human visual processing (AI Lab)     of
UNIX systems administrator & programmer/analyst (EECS DCO)         Michigan

```

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