the following is a homework question (that isn't going to be graded) and I'm not sure how to do it.

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I know that the solution trajectories cannot cross the H(x,y)=constant curves, but I'm not sure how to identify where the H(x,y)=constant curves are in the phase plane.

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    $\begingroup$ Just kidding I figured it out. A Hamiltonian system never has a sink or source equilibrium point, which means that (a) and (c) cannot be Hamiltonian. Boom. $\endgroup$ – Sam Sauce Dec 11 '14 at 5:51

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