Example 2. Reduce the following system of differential equations to a normal system:

$$
\left\{\begin{array}{r}
\frac{d^{2} x}{d t^{2}}-y=0 \\
t^{3} \frac{d y}{d t}-2 x=0
\end{array}\right.
$$
Solution. Let $x=x_{1}, \frac{d x}{d t}=x_{2}, y=x_{3}$. Then we will have $\frac{d x_{1}}{d t}=x_{2}$, $\frac{d y}{d t}=\frac{d x_{3}}{d t}$, and the given system will be reduced to the following normal third-order system:

$$
\left\{\begin{array}{l}
\frac{d x_{1}}{d t}=x_{2} \\
\frac{d x_{2}}{d t}=x_{3} \\
\frac{d x_{3}}{d t}=\frac{2 x_{1}}{t^{3}}
\end{array}\right.
$$