[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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