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MathGroup Archive 2000

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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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