4. For the initial value problem dy/dx = 3y^(2/3), y(2) = 0,
(a) does existence uniqueness Theorem 1 imply the existence of a unique solution? Explain.
(b) Which of the following functions are solutions to the above differential equation? Explain.
(b_1) y(x) = 0
(b_2) y(x) = (x - 2)^3
(b_3) y(x) = (x - alpha)^3, x < alpha
0, alpha <= x <= Beta
(x - Beta)^3, x > Beta
where alpha < 2 < Beta.
This solution shows how to use the uniqueness theorem to find the solution to an initial value problem in an attached Word document.