Can you solve for y in sin(y) - y = x√(2)?

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Discussion Overview

The discussion centers around the equation sin(y) - y = x√(2) and the possibility of solving for y. Participants explore the nature of solutions, including closed-form and numerical approaches, within the context of mathematical theory and applications.

Discussion Character

  • Exploratory, Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant questions the assumption that a closed-form solution for y can be found.
  • Another suggests that using the exponential form of sin(y) may lead to a solution involving the Lambert W function.
  • A different viewpoint expresses skepticism about the necessity of finding a closed-form solution, referencing the Kepler equation and suggesting that existing literature may provide insights.
  • It is proposed that iterative methods, power series, Fourier series, or numerical interpolation could be practical approaches to finding solutions.
  • One participant speculates on the relevance of periodic functions in natural phenomena, indicating that this particular function may have significance due to its occurrences.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the existence of a closed-form solution, and multiple competing views regarding the approach to solving the equation remain present.

Contextual Notes

The discussion highlights the complexity of the equation and the potential reliance on various mathematical methods, but does not resolve the assumptions or limitations inherent in the proposed approaches.

Who May Find This Useful

Readers interested in mathematical problem-solving, particularly in relation to transcendental equations and numerical methods, may find this discussion relevant.

wheepep
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sin(y) - y = x√(2)
solve for y
 
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What makes you think a closed-form solution for y can be found?
 
Maybe there exists a closed form solution exists, maybe not... But could I ask, what is the purpose for searching such solution?

I know, in celestial mechanics, the Kepler equation is same as this - at least after a change of variables - which means, you can take a look at literature, if you find something about it. As being so, I wouldn't use my time to kick the equation, as it is one of the most researched one in the world. Unless I wanted some sort of challenge, of course.

Anyhow, your choices for the solution will most likely be an iterative method, a power series or a Fourier series or interpolation of the numerical solution over the values of x under interest.
 
In general, periodic functions are of interest due to their frequent occurrence in natural phenomenon. As speculation, this particular function may be of interest due the times and places it occurs.
 

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