Question: 3. Consider the nonlinear system of ODES: x = y, y = -x- cx, Here, c> 0. Find and classify the linear stability type(s)

3. Consider the nonlinear system of ODES: x = y, y =

3. Consider the nonlinear system of ODES: x = y, y = -x- cx, Here, c> 0. Find and classify the linear stability type(s) of the fixed point(s), find a conserved quantity as the sum of the kinetic energy K.E. and the potential energy V(x), determine the nonlinear stability type of the fixed point at (0, 0), sketch trajectories in the (x, y) phase plane, and describe the motion of the particle in the potential V(x).

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