Initial value problem $dy/dx=y^{1/3}$, $y(0)=0$ has one of the following solution 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.
The answer is "none of the above". There are infinitely many solutions.

Pick any $\alpha &gt; 0$ and define $f_\alpha (x) = 0$ for $x \le \alpha$ and $f(x) = (2/3)^{3/2} (x-\alpha)^{3/2}$ for $x &gt; \alpha$. All these functions are solutions.
total $3$ solutions 

1.$y=0$ is also a solution. 

2.y=0 for $x \le 0$ and $y=(2/3x)^{(3/2)}$ (positive squ root) 

3.similarly consider neg squ root.