Let u(t) be a continuously differentiable function taking non-negative values for t > 0 satisfying u′(t)=3u(t)23 and u(0) = 0. Which of the following are possible solutions of the above equation?
(a) u(t) = 0
(b) u(t) = t3
(c) u(t)={0for0<t<1(t−1)3fort≥3
(d) u(t)={0for0<t<1(t−3)3fort≥3