Solving Equations with xy-yx = 1

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The equation xy - yx = 1 poses challenges for analytical solutions, leading many to suggest numerical methods using software like Mathematica or MATLAB. Historically, this equation has puzzled mathematicians for over 150 years, with recent advancements finally providing clarity. The discussion highlights the difficulty in finding a straightforward analytical method, suggesting that the solutions may be complex. Participants express frustration over the lack of accessible information on the equation's classification. For further details, resources like Wolfram may offer insights into its solutions.
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How can we solve an equation such as xy-yx = 1 without guessing?
 
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I'd solve that equation numerically, using mathematica or matlab.
 
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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?
 
Thread 'Video on imaginary numbers and some queries'

Thread 'Video on imaginary numbers and some queries'

Hi, I was watching the following video. I found some points confusing. Could you please help me to understand the gaps? Thanks, in advance! Question 1: Around 4:22, the video says the following. So for those mathematicians, negative numbers didn't exist. You could subtract, that is find the difference between two positive quantities, but you couldn't have a negative answer or negative coefficients. Mathematicians were so averse to negative numbers that there was no single quadratic...
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Thread 'Unit Circle Double Angle Derivations'

Thread 'Unit Circle Double Angle Derivations'

Here I made a terrible mistake of assuming this to be an equilateral triangle and set 2sinx=1 => x=pi/6. Although this did derive the double angle formulas it also led into a terrible mess trying to find all the combinations of sides. I must have been tired and just assumed 6x=180 and 2sinx=1. By that time, I was so mindset that I nearly scolded a person for even saying 90-x. I wonder if this is a case of biased observation that seeks to dis credit me like Jesus of Nazareth since in reality...
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Thread 'Imaginary Pythagoras'

Thread 'Imaginary Pythagoras'

I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...
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