If the function f(x,y) is continuous near the point (a,b), then at least one solution of the differential equation y'=f(x,y) exists on some open interval I containing the point x = a and, moreover, that if in of addition the partial derivative is continuous near (a,b) then this solution is unique on some (perhaps smaller) interval J. Determine whether existence of at least one solution of the given initial dy value problem is thereby guaranteed and, if so, whether uniqueness of that solution is guaranteed. dy dx = 6x¹y²:y(7)= -2 *** Select the correct choice below and fill in the answer box(es) to complete your choice. (Type an ordered pair.) O A. The theorem implies the existence of at least one solution because f(x,y) is continuous near the point This solution is unique because af dy O B. The theorem implies the existence of at least one solution because f(x,y) is continuous near the point continuous near that same point. OC. The theorem does not imply the existence of at least one solution because f(x,y) is not continuous near the point is also continuous near that same point. of However, this solution is not necessarily unique because = is not