Weird equation

[Lonewolf]

How can we solve an equation such as xy-yx = 1 without guessing?

[Pauly Man]

I'd solve that equation numerically, using mathematica or matlab.

[Lonewolf]

Is there no analytical method? Or is it just horrendously complicated?

[STAii]

This question was asked about 150 years ago.
It was only answered recently.
You can find more about its solution somewhere on Wolfram (http://mathworld.wolfram.com) .

[Lonewolf]

I can't find anything on it. Does anyone know what the class of equation is called?