Is there an easy way to show that the system:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

\begin{align}

x_1' &= p_{11} x_1 + p_{12} x_2 + \ldots + p_{1n} x_n \\

x_2' &= p_{21} x_1 + p_{22} x_2 + \ldots + p_{2n} x_n \\

\ldots &= \ldots \\

x_n' &= p_{n1} x_1 + p_{n2} x_2 + \ldots + p_{nn} x_n

\end{align}

[/tex]

must be equivalent to a single nth order differential equation, like

[tex]

a_n y^{(n)} + a_{n-1} y^{(n-1)} + \ldots + a_0 y_n = 0

[/tex]

All the [tex]p_{ij} = p_{ij}(t)[/tex] and [tex]a_i = a_i(t)[/tex]. In the case that n = 2, it's easy to show just by manipulation. I assume that it's true in general, but I can't find a slick way to do it.

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# From system of first-order to a single ODE

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