I've got an IVP I must discuss the application of the Existence & Uniqueness theorem to:

dy/dx = (x + y^2)^(2/3), y(-1) = 1

I'm just looking for help in figuring out where this function is not continuous. As far as I can make out it can be continuous everywhere, as in the one exceptional case I could imagine, where x + y^2 = 0, I would get (0)^2 = 0, then the cube root of 0 is also 0. Just want to check I'm not missing anything?

I'm also unsure if the solution I would get would be unique, as my dF/dy gives 2y/3(x + y^2)^(1/3), which when subbing in the initial point gives an undefined answer. Would that mean dF/dy is not bounded and therefore solution is not unique?