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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.

Math-learner
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    What about Wolfram Alpha? http://www.wolframalpha.com/input/?i=e%5Ey%2Bye%5Ey%2Be%5E%28-y%29%3D4-2cosx – rae306 Sep 23 '14 at 16:03

4 Answers4

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What about Wolfram Alpha or Desmos?

rae306
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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 $n = 0, \pm 1, \pm 2,...$

MartinG
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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}]}

UserX
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  • I wrote the code that you gave in mathematica but I received an error – Math-learner Sep 23 '14 at 16:20
  • I wrote the code that you gave in mathematica but I received the following error: – Math-learner Sep 23 '14 at 16:21
  • I wrote the code that you gave in mathematica but I received the following error: !(ContourPlot::"plnr" ((:)(\ )) "!((([ExponentialE]^(-y) + (
    ([ExponentialE]^y\ (((1 + y))))) + ((2\ ((Cos[x]))))))
    == 4) is not a machine-size real number at !({x, y}) =
    !({((-1.7142857142857144\)\), \(\(-2.))}).")     – Math-learner Sep 23 '14 at 16:22
  • The x_0,x_1,y_0,y_1 are the bounds of the graph, you have to insert numbers there. – UserX Sep 23 '14 at 17:53
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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.

Lucian
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