[SciPy-User] Functional nonlinear equation

Fabrice Silva silva@lma.cnrs-mrs...
Sun Dec 27 10:00:08 CST 2009

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@lma.cnrs-mrs.fr>
LMA UPR CNRS 7051 - équipe S2M

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