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

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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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