Can x²+2xsin(xy)+1=0 be solved for a single numerical solution?

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Discussion Overview

The discussion revolves around the equation x² + 2xsin(xy) + 1 = 0 and whether it can be solved for a single numerical solution. Participants explore the graphical representation of the function and its implications for finding solutions.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant suggests that the graph of the function will resemble an arcsine shape and proposes solving for y.
  • Another participant questions the shape of the graph and emphasizes the need to understand turning points, intercepts, and asymptotes for analysis.
  • A later reply indicates that making sin(xy) the subject and taking the arcsine could restrict the allowed values of x.
  • There is mention of the function's relevance in the context of integrating factors, although the specifics of this connection are not elaborated upon.

Areas of Agreement / Disagreement

Participants express differing views on the graph's shape and the implications for solving the equation, indicating that multiple competing perspectives remain without a consensus on a single numerical solution.

Contextual Notes

Participants note the importance of understanding turning points and intercepts, but do not resolve the mathematical steps or assumptions necessary for a complete analysis.

uppaladhadium
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x²+2xsin(xy)+1=0
 
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You mean - what is the graph of the function?
http://www.learner.org/courses/teachingmath/grades9_12/session_05/index.html

the plot of y(x) vs x will be an arcsine. solve for y.
 
I mean what is the shape of the graph plotted for the given equation
 
well then: the plot of y(x) vs x will be an arcsine shape.

Are you having trouble solving for y?
(If so - make sin(xy) the subject and take the arcsine of both sides.)
... which kinda restricts allowed values of x doesn't it.

What you need are turning points, intercepts, and asymptotes - how would you normally find them?

note: this sort of function tends to come up in the context of integrating factors.
 
Last edited:

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