I'm working on the equation $yx = e^{x+y}$. I'm trying to approximate the roots using Newton's method (solving for y), but I can't figure it out and examples only offer system of equations. I'm not given any initial values or whatsoever. Anyone can help me out? I just don't see how I can even set it up.
2026-03-27 03:56:09.1774583769
Solving multivariate function using Newton's method
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The solution of the equation $$yx = e^{x+y}$$ is given as $$y=-W\left(-\frac{e^x}{x}\right)$$ where $W(.)$ is Lambert function.
Have a look at the "numerical evaluation" section to see Newton method.