$\dot{x}(t)=3x(t)^\frac{2}{3}$ ; $t\geq0$ ; $x(0)=0$ How can I say id this differential equation have solution and if its unique:

$\dot{x}(t)=3x(t)^\frac{2}{3}$ ; $t\geq0$ ; $x(0)=0$

I stuck in this problem some help please.
Since $f(x,t)=x^{2/3}$ is continuous on $\Bbb{R}\times\Bbb{R}$, then using Peano's theorem, this Cauchy problem has solutions. In fact, it has infinitely many solutions, namely,
for $c\geq0$ the function $\psi_c:[0,+\infty)\longrightarrow \Bbb{R}$ defined by
$$
\psi_c(t)=\left\{\matrix{0&amp;\hbox{if}&amp; 0\leq t\leq c,\cr
(t-c)^3&amp;\hbox{if}&amp;c&lt;t\phantom{\leq c}.}\right.
$$ 
is clearly a solution to the proposed Cauchy problem.
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No need to read anything...
\begin{align}
\int_{{\rm x}\pars{0}}^{{\rm x}\pars{t}}{\dd\xi \over 3\xi^{2/3}} = \int_{0}^{t}\dd\tau
\quad\imp\quad{\rm x}^{1/3}\pars{t} - {\rm x}^{1/3}\pars{0} = t - 0
\end{align}


  $$
\color{#00f}{\large{\rm x}\pars{t} = t^{3}}
$$