Solving Equations with xy-yx = 1

In summary, the equation xy-yx = 1 is a non-linear equation involving two variables and a constant value of 1. It can be solved using algebraic or graphical methods and has infinite possible solutions, which are usually non-integer values. It can also be solved using calculus and has applications in various fields, such as physics, engineering, and economics.
  • #1
Lonewolf
336
1
How can we solve an equation such as xy-yx = 1 without guessing?
 
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  • #2
I'd solve that equation numerically, using mathematica or matlab.
 
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  • #3
Is there no analytical method? Or is it just horrendously complicated?
 
  • #4
This question was asked about 150 years ago.
It was only answered recently.
You can find more about its solution somewhere on Wolfram .
 
  • #5
I can't find anything on it. Does anyone know what the class of equation is called?
 

FAQ: Solving Equations with xy-yx = 1

What is the equation xy-yx = 1?

The equation xy-yx = 1 is a mathematical equation involving two variables, x and y, and a constant value of 1. It is an example of a non-linear equation as the variables are not raised to a power and the terms are not directly proportional.

How do you solve for x and y in xy-yx = 1?

To solve for x and y in xy-yx = 1, you can use algebraic methods such as substitution or elimination. You can also graph the equation to find the points where the line crosses the x and y axes, which represent the solutions for x and y.

What are the possible solutions for xy-yx = 1?

The possible solutions for xy-yx = 1 are infinite, as there are an infinite number of values for x and y that can satisfy the equation. However, in most cases, the solutions will be non-integer values.

Can the equation xy-yx = 1 be solved using calculus?

Yes, the equation xy-yx = 1 can be solved using calculus methods such as differentiation and integration. However, these methods may be more complex and not necessary for finding the solutions.

How is the equation xy-yx = 1 used in real-world applications?

The equation xy-yx = 1 may be used in physics and engineering to model non-linear systems, such as chemical reactions or biological processes. It can also be used to analyze economic and financial systems that do not follow a linear trend.

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