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sin(y) - y = x√(2)

wheepep

New member
Nov 25, 2016
9
sin(y) - y = x√(2)
solve for y
 

skeeter

Well-known member
MHB Math Helper
Mar 1, 2012
935
What makes you think a closed-form solution for y can be found?
 

Country Boy

Well-known member
MHB Math Helper
Jan 30, 2018
756

Theia

Well-known member
Mar 30, 2016
115
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.
 

Greg

Perseverance
Staff member
Feb 5, 2013
1,404
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.