With C an arbitrary constant, find a solution to the differential equation given: (csc x)y' + csc y = 0?

With C an arbitrary constant, find a solution to the differential equation given: (csc x)y' + csc y = 0?








a. y = Cx^-4





b. y = Cx^-1/4





c. y = Cx^1/4





d. y = Cx^4





e. sin y + cos x = C





f. cos y + sin x = C





g. cos y - sin x = C





h. sin y - cos x = C





or is it none of these ?

With C an arbitrary constant, find a solution to the differential equation given: (csc x)y' + csc y = 0?
dy/dx = -csc y / csc x





dy/dx = -sinx / sin y





sin y dy = -sinx dx





∫sin y dy = -∫sinx dx





-cos y = cos x + C





cos x + cos y = C