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\(\displaystyle

\begin{cases}

y''(t)=-\frac{y(t)}{||y(t)||^3} \ , \forall t >0

\\

y(0)= \Big(\begin{matrix} 1\\0\end{matrix} \Big) \

\text{and}

\

y'(0)= \Big(\begin{matrix} 0\\1\end{matrix} \Big)

\end{cases}

\\

y(t) \in \mathbb{R}^2 \ \forall t

\)

Thanks in advance ^^