Re: Enquirey

• To: mathgroup at smc.vnet.net
• Subject: [mg74823] Re: Enquirey
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Fri, 6 Apr 2007 04:26:21 -0400 (EDT)
• Organization: The Open University, Milton Keynes, UK
• References: <ev2anc\$k85\$1@smc.vnet.net>

```Rita Ray wrote:
> I am trying to solve two equation with two unknowns. I am using
> Mathematica 5.2.  Below is my program
>
>
> Solve[{a*Exp[2*w]-a^2*Exp[w+(x-y)*z]+a^2*Exp[w-(x-y)*z]-a*Exp[w+(x-y)*z]-a*=
> Exp[w-(x-y)*z]+a^2*Exp[2*(x-y)]+a-a^2+a^2*x*Exp[w+(x-y)*z]
> +a^2*x*Exp[w-(x-y)*z]-a*x*Exp[w+(x-y)*z]-a*x*Exp[w-(x-y)*z]+2*a*x-2*a^2*x-(=
> (a^3*w*Exp[w+(x-y)*z])/z)-((a^3*w*Exp[w-(x-y)*z])/z)+((a^2*w*Exp[w+(x-y)*z]=
> )/z)+((a^2*w*Exp[w-(x-y)*z])/z)-((2*a^2*w)/z)+((2*a^3*w)/z)====0,-((a*Exp[-=
> w+(x-y)*z]*z*(-((1-a)*w)-2*w*a^2+2*w*a^3+a^2*w*Exp[w-(x-y)*z]-a^3*w*Exp[w-(=
> x-y)*z]+a^2*w*Exp[w+(x-y)*z]-a^3*w*Exp[w+(x-y)*z]+a*z-a^2*z+a*z*Exp[2*w]+a^=
> 2*z*Exp[2*(x-y)]-a*z*Exp[w-(x-y)*z]+a^2*z*Exp[w-(x-y)*z]-a*z*Exp[w+(x-y)*z]=
> -a^2*z*Exp[w+(x-y)*z]+2*a*x*z-2*a^2*x*z-a*x*z*Exp[w-(x-y)*z]+a^2*x*z*Exp[w-=
> (x-y)*z]-a*x*z*Exp[w+(x-y)*z]+a^2*x*z*Exp[w+(x-y)*z]))/(a*Exp[-w+(x-y)*z]+(=
> 1-a)*Exp[-w-(x-y)*z]))-(a*Exp[-w+(x-y)*z]*((1-a)*z*Exp[-w-(x-y)*z]-a*z*Exp[=
> -w+(x-y)*z])*(-((1-a)*w)-2*w*a^2+2*w*a^3+a^2*w*Exp[w-(x-y)*z]-a^3*w*Exp[w-(=
> x-y)*z]+a^2*w*Exp[w+(x-y)*z]-a^3*w*Exp[w+(x-y)*z]+a*z-a^2*z+a*z*Exp[2*w]+a^=
> 2*z*Exp[2*(x-y)]-a*z*Exp[w-(x-y)*z]+a^2*z*Exp[w-(x-y)*z]-a*z*Exp[w+(x-y)*z]=
> -a^2*z*Exp[w+(x-y)*z]+2*a*x*z-2*a^2*x*z-a*x*z*Exp[w-(x-y)*z]+a^2*x*z*Exp[w-=
> (x-y)*z]-a*x*z*Exp[w+(x-y)*z]+a^2*x*z*Exp[w+(x-y)*z]))/(a*Exp[-w+(x-y)*z]+(=
> 1-a)*Exp[-w-(x-y)*z])^2+(a*Exp[-w+(x-y)*z]*(-2*a^2*z*Exp[2*(x-y)]+a^2*w*z*E=
> xp[w-(x-y)*z]-a^3*w*z*Exp[w-(x-y)*z]-a^2*w*z*Exp[w+(x-y)*z]+a^3*w*z*Exp[w+(=
> x-y)*z]-a*z^2*Exp[w-(x-y)*z]+a^2*z^2*Exp[w-(x-y)*z]+a*z^2*Exp[w+(x-y)*z]+a^=
> 2*z^2*Exp[w+(x-y)*z]-a*x*z^2*Exp[w-(x-y)*z]+a^2*x*z^2*Exp[w-(x-y)*z]
> +a*x*z^2*Exp[w+(x-y)*z]-a^2*x*z^2*Exp[w+(x-y)*z]))/(a*Exp[-w+(x-y)*z]+(1-a)=
> *Exp[-w-(x-y)*z])====0},{x,y}]
>
>
> Thank you.
>
> Rita Ray.
>
> Ph.D. student
>

Four equal signs in a row (i.e. ====) does not mean anything in
Mathematica. To set up an equation, what you want to use is two equal
signs in a row (i.e. ==).

Since "Solve deals primarily with linear and polynomial equations
message, "Reduce::nsmet: This system cannot be solved with the methods
available to Reduce, you might want to try a different approach, like a
numerical solution with NSolve.

eqn1 = (-a)*Exp[2*w] - a^2*Exp[w + (x - y)*z] +
a^2*Exp[w - (x - y)*z] - a*Exp[w + (x - y)*z] -
a*Exp[w - (x - y)*z] + a^2*Exp[2*(x - y)] + a -
a^2 + a^2*x*Exp[w + (x - y)*z] +
a^2*x*Exp[w - (x - y)*z] -
a*x*Exp[w + (x - y)*z] - a*x*Exp[w - (x - y)*z] +
2*a*x - 2*a^2*x - (a^3*w*Exp[w + (x - y)*z])/z -
(a^3*w*Exp[w - (x - y)*z])/z +
(a^2*w*Exp[w + (x - y)*z])/z +
(a^2*w*Exp[w - (x - y)*z])/z - (2*a^2*w)/z +
(2*a^3*w)/z == 0;

eqn2 = -((a*Exp[-w + (x - y)*z]*z*(-((1 - a)*w) -
2*w*a^2 + 2*w*a^3 + a^2*w*
Exp[w - (x - y)*z] - a^3*w*
Exp[w - (x - y)*z] + a^2*w*
Exp[w + (x - y)*z] - a^3*w*
Exp[w + (x - y)*z] + a*z - a^2*z +
a*z*Exp[2*w] + a^2*z*Exp[2*(x - y)] -
a*z*Exp[w - (x - y)*z] +
a^2*z*Exp[w - (x - y)*z] -
a*z*Exp[w + (x - y)*z] -
a^2*z*Exp[w + (x - y)*z] + 2*a*x*z -
2*a^2*x*z - a*x*z*Exp[w - (x - y)*z] +
a^2*x*z*Exp[w - (x - y)*z] -
a*x*z*Exp[w + (x - y)*z] + a^2*x*z*
Exp[w + (x - y)*z]))/
(a*Exp[-w + (x - y)*z] + (1 - a)*
Exp[-w - (x - y)*z])) -
(a*Exp[-w + (x - y)*z]*
((1 - a)*z*Exp[-w - (x - y)*z] -
a*z*Exp[-w + (x - y)*z])*(-((1 - a)*w) -
2*w*a^2 + 2*w*a^3 + a^2*w*Exp[w - (x - y)*z] -
a^3*w*Exp[w - (x - y)*z] +
a^2*w*Exp[w + (x - y)*z] -
a^3*w*Exp[w + (x - y)*z] + a*z - a^2*z +
a*z*Exp[2*w] + a^2*z*Exp[2*(x - y)] -
a*z*Exp[w - (x - y)*z] +
a^2*z*Exp[w - (x - y)*z] -
a*z*Exp[w + (x - y)*z] -
a^2*z*Exp[w + (x - y)*z] + 2*a*x*z -
2*a^2*x*z - a*x*z*Exp[w - (x - y)*z] +
a^2*x*z*Exp[w - (x - y)*z] -
a*x*z*Exp[w + (x - y)*z] +
a^2*x*z*Exp[w + (x - y)*z]))/
(a*Exp[-w + (x - y)*z] + (1 - a)*
Exp[-w - (x - y)*z])^2 +
(a*Exp[-w + (x - y)*z]*(-2*a^2*z*Exp[2*(x - y)] +
a^2*w*z*Exp[w - (x - y)*z] -
a^3*w*z*Exp[w - (x - y)*z] -
a^2*w*z*Exp[w + (x - y)*z] +
a^3*w*z*Exp[w + (x - y)*z] -
a*z^2*Exp[w - (x - y)*z] +
a^2*z^2*Exp[w - (x - y)*z] +
a*z^2*Exp[w + (x - y)*z] +
a^2*z^2*Exp[w + (x - y)*z] -
a*x*z^2*Exp[w - (x - y)*z] + a^2*x*z^2*
Exp[w - (x - y)*z] + a*x*z^2*
Exp[w + (x - y)*z] - a^2*x*z^2*
Exp[w + (x - y)*z]))/(a*Exp[-w + (x - y)*z] +
(1 - a)*Exp[-w - (x - y)*z]) == 0;

Reduce[{eqn1, eqn2}, {x, y}]

Regards,
Jean-Marc

```

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