# [SciPy-User] Functional nonlinear equation

Lou Pecora lou_boog2000@yahoo....
Sun Dec 27 09:21:22 CST 2009

```From: Dorian <wizzard028wise@gmail.com>
To: SciPy Users List <scipy-user@scipy.org>
Sent: Sun, December 27, 2009 9:35:28 AM
Subject: Re: [SciPy-User] Functional nonlinear equation

Is there any way to solve it in the functional form ?
I do not have "mathematica" to do it.
Thanks for the plot suggestion.

Dorian

On Sun, Dec 27, 2009 at 3:00 PM, Richard <reg8@cornell.edu> wrote:

I assume , x,y,a are real variables.  I would try using a contour plotting program. There is probably something like that already available in matplotlib. You would evaluate f(x,y) on a grid of (x,y) values and the contouring program will perform an efficient search for the points in the x,y plane where f = <any constant>.
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>Richard
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>On Dec 27, 2009, at 7:42 AM, Dorian wrote:
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>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
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>>where  "a"  is positive parameter.
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>>If there is a way to plot  f(x,y) for different values of "a"
>>it will be very appreciated.
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>>Dorian
>>>>_______________________________________________
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>Am I missing something?  (It is early).  Just do some algebra and get:
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>x = y/(y^(1/a-1)/a - 1)^(1/(1/a-1))
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>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?
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>Bonus question #1:  what happens when a=1?
>Bonus question #2:  what happens when y^(1/a-1)=a ?
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> -- Lou Pecora, my views are my own.
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>

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