[SciPy-User] Functional nonlinear equation

[Lou Pecora]

----- Original Message ----
From: Fabrice Silva <silva at lma.cnrs-mrs.fr>
To: scipy-user at scipy.org
Sent: Sun, December 27, 2009 11:00:08 AM
Subject: Re: [SciPy-User] Functional nonlinear equation

Le dimanche 27 décembre 2009 à 07:21 -0800, Lou Pecora a écrit :


> Hi  all,
> How do I solve  the following functional nonlinear equation 
> f(x,y)= (-1/a^2)*(x*y)^(1/a-1)+(1/a)*x^(1/a-1)+(1/a)*y^(1/a-1) =0
> where  "a"  is positive parameter.  
>         > 
> Am I missing something?  (It is early).  Just do some algebra and get:
>         x = y/(y^(1/a-1)/a - 1)^(1/(1/a-1))
> Please check my math.  But you can solve for either x or y in terms of
> y or x, respectively. Is that what you want?

You may be careful with assertion like (x^b)^(1/b)=x which may be false
for example sqrt(x**2)=abs(x)!=x

The consequence is that the locus given by Charles (hyperbola) may not
be the entire set of solutions. Plotting the function may help to
'guess' others solutions.

-- 
Fabrice Silva <silva at lma.cnrs-mrs.fr>


Right.  And for negative x or y values we are working on the complex plane (sort of a generalization to you point).  There are plenty of angles in this problem. I just mentioned the singularities.    Nothing against plotting the function (for real values), but writing explicit solutions can give you more insight, too.

 -- Lou Pecora, my views are my own.