MATB44H3 Lecture Notes - Lecture 3: Ordinary Differential Equation

version of Theorem 1 says nal, A more detailed tion 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 addition the partial derivative af/ay is continuous near (a, b), then this solution is unique on some (perhaps smaller) interval J. In Problems 11 through 20, de- termine 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.