Question

Does Peano’s theorem apply to establish existence of at least one solution, for the problem below? Please carefully check
the hypothesis of the theorem, which is continuity of f(x, y) on a box with center x = 0, y = 1.
y′= 3(y − 1)^(1/3), y(0) = 1.

Answer 1

What are you finding difficult here?

Answer 2

don't really understand what its asking

Answer 3

What is the statement of Peano's Theorem? What exactly is the hypothesis that must be satisfied? Your question is asking you if the ODE in the question satisfies that hypothesis.