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(Solved): 3.6 Show that the system \[ \begin{array}{l} x^{\prime}=x+16 y, \\ y^{\prime}=-8 x-y \end{array} \ ...



3.6 Show that the system
\[
\begin{array}{l}
x^{\prime}=x+16 y, \\
y^{\prime}=-8 x-y
\end{array}
\]
is a Hamiltonian system,

3.6 Show that the system \[ \begin{array}{l} x^{\prime}=x+16 y, \\ y^{\prime}=-8 x-y \end{array} \] is a Hamiltonian system, find the equations for the orbits, and sketch the phase plane diagram.


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