Express the following \(n\) th-order differential equation as a system of \(n\) first-order differential equations:

\[a_{n} \frac{d^{n} x}{d t^{n}}+a_{n-1} \frac{d^{n-1} x}{d t^{n-1}}+\cdots+a_{1} \frac{d x}{d t}=g(x, t)\]