       AW: implicit function

• To: mathgroup at smc.vnet.net
• Subject: [mg24244] AW: [mg24218] implicit function
• From: Matthias.Bode at oppenheim.de
• Date: Mon, 3 Jul 2000 20:39:24 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Mr. Sangio Lee wrote:
> I'm a graduate student in South Korea for Physics and my name is Sangjo
> Lee.
>
> Following is my problem.
> there is one implicit function like this :
> ( (1-y) / x + 1/m )^x = y Exp[f(x) z]  / m^x     where     f(x) = 1 + (x
> - 1)/( 2( x + 1) )
> x, y is variable and other symbols are constants.
> I want to get the numerical y value when x is  -10 < x < 10.
>
> well...
> I am looking forward to seeing your e-mail.
> Thank you.
>
> yours Sincerely.
>
> from  S. Korea
>
Dear Colleague,

as m and z are constants I assign them - for example's sake - the values E
and Pi respectively;
fortunately the rest is almost as simple:

m = E;
z = Pi;
Table[N[Solve[((1 - y)/x + 1/m)^x ==
(y*Exp[1 +
((x - 1)*z)/
(2*(x + 1))])/m^x, y]], {x, 2, 3}]//Flatten

{y -> 0.5582091478296327,
y -> 5.397365681566638,
y -> 0.5074441647195549,
y ->
2.901735402911711 -
3.150434512934943*I,
y ->
2.901735402911711 +
3.150434512934943*I}

Your function - which I hope I did not misrepresent - does however not
appear to be very "smooth".

Hoping that the solution is useful nevertheless, I remain

Yours sincerely,

Matthias Bode

```

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