### Simple ODE Problem

Please give me a step-by-step solution to this attached ODE. Consider the following system: x' = -2y y' = x/2 a. Show that this system is a Hamiltonian system. b. Us a Hamiltonian to sketch the phase portrait for this system.

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Please give me a step-by-step solution to this attached ODE. Consider the following system: x' = -2y y' = x/2 a. Show that this system is a Hamiltonian system. b. Us a Hamiltonian to sketch the phase portrait for this system.

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Convert {see attachment} into a system of differential equations and classify the resulting system

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Please see the attached file for full problem description. --- Here is the problem: Find the center of mass of the region bounded by the parabola y = 8 -2x^2 and the x-axis a) if the density lambda is constant and b) if the density lambda = 3y

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This question is part of a study guide for my final test. Solve the following initial value problem. (see attached for problem) Thank you

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View attachment

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Solve the initial value problem dy/dx=(3x^2+4x+2)/[2(y-1)], y(0)=-1