I came across the following problem which says:

The initial value problem $y'=y^{1/3}$, $y(0)=0$ has: 

(a) a unique solution,

(b) exactly two solutions,

(c)exactly three solutions,

(d)no solution. 

The solution of the problem is given by: $2x=3y^{2/3}$. But I could not come to a conclusion. Clearly, (d) can not be true. But i am not sure about the other options. It will be helpful if someone throws light on it. Thanks in advance.