a) Show the system is Hamiltonian with 𝐻𝐻(𝑥𝑥, 𝑦𝑦) = sin (𝑥𝑥𝑥𝑥) as it’s function. b) Draw the phase plane (directional fi

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a) Show the system is Hamiltonian with 𝐻𝐻(𝑥𝑥, 𝑦𝑦) = sin (𝑥𝑥𝑥𝑥) as it’s function. b) Draw the phase plane (directional field using software) c) Find the solution curve that passes through the point (1, 𝜋𝜋 2 ) and draw it on the phase plane from part b) (do not solve the equation for y or x)