If the function f(x, y) is continuous near the point (a, b), then at least one solution of the differential equation y primeequalsf(x, y) exists on some open interval I containing the point xequalsa and, moreover, that if in addition the partial derivative StartFraction partial derivative f Over partial derivative y EndFraction 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 value problem is thereby guaranteed and, if so, whether uniqueness of that solution is guaranteed. StartFraction dy Over dx EndFraction equalsRootIndex 5 StartRoot y EndRoot; y(0)equals1