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

[uppaladhadium]

x²+2xsin(xy)+1=0

 

[Simon Bridge]

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.

 

[uppaladhadium]

I mean what is the shape of the graph plotted for the given equation

 

[Simon Bridge]

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.

 

[CellCoree]

can be solved using various methods, such as factoring, completing the square, or using the quadratic formula. However, due to the presence of the variable xy in the sine term, it is not possible to find a single numerical solution for x. Instead, the equation can be solved for different values of y, resulting in a set of equations that can be graphed to show the relationship between x and y. This can help us understand the behavior of the equation and how it changes as y varies. Additionally, numerical methods such as iteration or approximation can be used to find approximate solutions for x. It is important to note that in mathematics, not all equations have a single solution and some may only have solutions in certain ranges or for certain values of variables. Therefore, the solution to this equation is not a single number, but rather a relationship between x and y.