Solving Equations with xy-yx = 1

  • Context: Undergrad 
  • Thread starter Thread starter Lonewolf
  • Start date Start date
  • Tags Tags
    Solving equations
Click For Summary

Discussion Overview

The discussion revolves around the equation xy - yx = 1, exploring methods for solving it. Participants consider both numerical and analytical approaches, as well as the historical context of the equation.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant inquires about solving the equation without guessing.
  • Another participant suggests a numerical solution using software like Mathematica or MATLAB.
  • A different participant questions the existence of an analytical method, expressing concern about potential complexity.
  • One participant notes that the question has historical significance, mentioning that it was only recently answered.
  • A participant expresses difficulty in finding information about the equation, asking for the class of the equation.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the methods for solving the equation, with some favoring numerical approaches while others seek analytical solutions. The discussion remains unresolved regarding the classification and solution methods.

Lonewolf
Messages
329
Reaction score
1
How can we solve an equation such as xy-yx = 1 without guessing?
 
Mathematics news on Phys.org
I'd solve that equation numerically, using mathematica or matlab.
 
Last edited:
Is there no analytical method? Or is it just horrendously complicated?
 
This question was asked about 150 years ago.
It was only answered recently.
You can find more about its solution somewhere on Wolfram .
 
I can't find anything on it. Does anyone know what the class of equation is called?
 

Similar threads

High School Adding 'x' to 'xy' for Resultant <=1: A Table Guide
  • · Replies 18 ·
Replies
18
Views
3K
MHB What is the range and inverse of the function y = 1/x?
  • · Replies 3 ·
Replies
3
Views
2K
MHB Solving System of Equalities: x^2-y\sqrt xy & y^2-x\sqrt xy =3
  • · Replies 2 ·
Replies
2
Views
1K
MHB Solve System of Equalities: x^2+xy+y^2, x^2+xz+z^2, y^2+yz+z^2
  • · Replies 7 ·
Replies
7
Views
3K
Undergrad What is the Unique Linear Functional in $M_n(\Bbb F)$ Satisfying Two Conditions?
  • · Replies 1 ·
Replies
1
Views
3K
Exercise on law of total expectation
  • · Replies 1 ·
Replies
1
Views
2K
Calculating x Position of a Moving Object
  • · Replies 10 ·
Replies
10
Views
3K
Undergrad Solving a System of Nonlinear Equations Symbolically
  • · Replies 9 ·
Replies
9
Views
3K
Determine the mean square error of a simple distribution
  • · Replies 4 ·
Replies
4
Views
2K
MHB Solving $x^3+y^3=7$ and $x^2+y^2+x+y+xy=4$ System of Equations
  • · Replies 1 ·
Replies
1
Views
1K