[SciPy-User] Functional nonlinear equation
Sun Dec 27 10:21:47 CST 2009
----- Original Message ----
From: Fabrice Silva <firstname.lastname@example.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 <email@example.com>
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.
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