Final answer:
The differential equation given, assuming it is meant to be dy/dx = 7sin(x), is considered separable because the variables can be isolated on opposite sides of the equation.
Step-by-step explanation:
The differential equation as given, dy/dx = 7sin, appears incomplete and may contain a typo. However, if we assume that it is meant to represent dy/dx = 7sin(x), then this equation would be considered separable. To determine if a differential equation is separable, each variable and its derivatives must be able to be isolated on opposite sides of the equation.
In a separable equation, variables can be separated such that all terms with x are on one side and all terms with y are on another. Looking at the function dy/dx = 7sin(x), if we rearrange it to dy = 7sin(x)dx, we've effectively separated the variables.
Regarding the information provided about Yk (x) = Bk sin kx, it pertains to a different context involving normalization conditions in functions that might arise in mathematical physics or engineering, specifically when Bk is nonzero, which is unrelated to whether the given differential equation is separable or not.