ASKSAGE: Sage Q&A Forum - Individual question feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Fri, 07 Apr 2017 12:20:35 -0500Solving equations for the parmatershttps://ask.sagemath.org/question/37208/solving-equations-for-the-parmaters/ $$ xe^{-1/y}=0.6$$ and $$xye^{-1}=1.2$$
I am trying to solve this equations for approximate value of the parameters $x$ and $y$ using SageMath. any help would be appreciated. Thu, 06 Apr 2017 20:39:11 -0500https://ask.sagemath.org/question/37208/solving-equations-for-the-parmaters/Comment by vdelecroix for <p>$$ xe^{-1/y}=0.6$$ and $$xye^{-1}=1.2$$ </p>
<p>I am trying to solve this equations for approximate value of the parameters $x$ and $y$ using SageMath. any help would be appreciated. </p>
https://ask.sagemath.org/question/37208/solving-equations-for-the-parmaters/?comment=37215#post-id-37215What did you try?Fri, 07 Apr 2017 02:06:47 -0500https://ask.sagemath.org/question/37208/solving-equations-for-the-parmaters/?comment=37215#post-id-37215Answer by dan_fulea for <p>$$ xe^{-1/y}=0.6$$ and $$xye^{-1}=1.2$$ </p>
<p>I am trying to solve this equations for approximate value of the parameters $x$ and $y$ using SageMath. any help would be appreciated. </p>
https://ask.sagemath.org/question/37208/solving-equations-for-the-parmaters/?answer=37228#post-id-37228The two equations allow a quick elimination of $x>0$. We can than numerically solve the remaining one equation in the remaining single variable $y$. The following code may help to get the relevant information, adapted to my taste:
sage: f(y) = log(y) +1/y -1 - log(2)
sage: f
y |--> 1/y - log(2) + log(y) - 1
sage: plot( f, 0.2, 0.5 )
Launched png viewer for Graphics object consisting of 1 graphics primitive
sage: find_root( f, 0.2, 0.4 )
0.3733646177016173
sage: gp( "solve( y=0.2, 0.4, %s )" %f(y) )
0.37336461770167408424844843667927059501
(The value for $x$ is easily found from the second equation.)Fri, 07 Apr 2017 12:20:35 -0500https://ask.sagemath.org/question/37208/solving-equations-for-the-parmaters/?answer=37228#post-id-37228