Given system like ##\begin{bmatrix}(adsbygoogle = window.adsbygoogle || []).push({});

x'(t)\\

y'(t)\\

\end{bmatrix}

=

\begin{bmatrix}

a & b \\

c & d \\

\end{bmatrix}

\begin{bmatrix}

x(t)\\

y(t)\\

\end{bmatrix}## can be rewritten as ##(-1)u''(t) + (bd)u'(t) + (ad+c)u(t) = 0## with ##\begin{bmatrix}

x(t)\\

y(t)\\

\end{bmatrix}

=

\begin{bmatrix}

u(t)\\

u'(t)\\

\end{bmatrix}##

In other words, if a diff equation of 2nd order can be disassembled in a sytem of 1nd order, thus a system of 1nd order can be assembled in a diff equation of 2nd order, correct? This way, I don't need to find the eigenvalues and eigenvectors...

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# Solution for system of diff equations

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