How to sketch the graph of an implicit in two dimentional space xy?

Question

I am looking for a software able to sketch the graph of $y = y(x),$ where: ${e^y} + y{e^y} + {e^{ - y}} = 4 - 2\cos x$

your help is highly appreciated, thank you.

Answer 1

What about Wolfram Alpha or Desmos?

Answer 2

Mathematica can do this. The code is {ContourPlot[E^(-y) + E^y (1 + y) + 2 Cos[x] == 4, {x, x_0, x_1}, {y, y_0, y_1}]}

Answer 3

A simple solution would be to plot (for a suitable range of $y$) $$ x(y) = \pm\cos^{-1}\left(2 - \tfrac{1}{2}({e^y} + y{e^y} + {e^{ - y}})\right) +2\pi n $$ for $n = 0, \pm 1, \pm 2,...$

Answer 4

The graphic of $y=y(x)$ is the same as that of $x=x(y)$, rotated by $90^\circ$. The whole idea is to find the intervals for which the left hand side lies between $4-2=2$ and $4+2=6$, since $|\cos x|\le1$. Otherwise, $\arccos$ might inevitably return an error. Which is why I would recommend GeoGebra, which doesn't seem to have these sort of issues.