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Why is it impossible to solve y explicitly in this equation?

  1. Mar 13, 2013 #1

    How would you even graph a function like this if you can't solve for y explicitly?
  2. jcsd
  3. Mar 13, 2013 #2


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    Make a table of values. Pick some y-values and solve each of them for x.
  4. Mar 13, 2013 #3
    Why is it impossible to solve y explicitly in this equation?
  5. Mar 13, 2013 #4


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    The presence of sin y. Trig functions are transcendental and cannot be solved using algebraic methods alone.
  6. Mar 13, 2013 #5
    With this in mind (and I agree) one cannot solve this either,
    [tex] \sin{y} = x [/tex]
    We have to invent a special function, the inverse sine, to solve it. By that same logic, we can invent a special function to solve the original equation. But it would be no more "solved" than using the inverse sine function to solve my equation above.
  7. Mar 13, 2013 #6


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    you can graph [itex]x[/itex] as a function of [itex]y[/itex] explicitly, then turn the graph by 90° and flip (mirror image) the rotated graph.

    i do not think there is a closed form solution to

    [tex] y + a \sin(y) = x [/tex]

    but you can still solve it numerically, as long as [itex] |a| \le 1 [/itex]. there are places in the [itex]y=f(x)[/itex] function where the slope is infinite, but only on a single point. sorta like the real function [itex] y = x^{1/3} [/itex].
  8. Mar 13, 2013 #7


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    Have you tried to apply the explicit function theorem to see if a local solution for y is
  9. Mar 13, 2013 #8


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    Graph y= x+ sin(x), then flip the x and y axes.
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