Someone can explain me how to get the general solution for this system of ODE of second order with constant coeficients:[tex](adsbygoogle = window.adsbygoogle || []).push({});

\begin{bmatrix}

a_{11} & a_{12}\\

a_{21} & a_{22}\\

\end{bmatrix}

\begin{bmatrix}

\frac{d^2x}{dt^2}\\

\frac{d^2y}{dt^2}\\

\end{bmatrix}

+

\begin{bmatrix}

b_{11} & b_{12}\\

b_{21} & b_{22}\\

\end{bmatrix}

\begin{bmatrix}

\frac{dx}{dt}\\

\frac{dy}{dt}\\

\end{bmatrix}

+

\begin{bmatrix}

c_{11} & c_{12}\\

c_{21} & c_{22}\\

\end{bmatrix}

\begin{bmatrix}

x\\

y\\

\end{bmatrix}

=

\begin{bmatrix}

0\\

0\\

\end{bmatrix}

[/tex]

OBS: source of the doubt: https://es.wikipedia.org/wiki/Movimiento_armónico_complejo

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# System of ODE of second order

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