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

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The equation x² + 2xsin(xy) + 1 = 0 can be analyzed by plotting y(x) against x, resulting in an arcsine shape. To solve for y, one can isolate sin(xy) and apply the arcsine function, though this restricts the permissible values of x. Identifying turning points, intercepts, and asymptotes is crucial for understanding the graph's behavior. Such functions often arise in the context of integrating factors in calculus. Overall, the discussion emphasizes the importance of graphical analysis and algebraic manipulation in solving the equation.
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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.
 
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