3. Consider the nonlinear system of ODES: x = y, y = -x- cx, Here, c>...

 

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3. Consider the nonlinear system of ODES: x = y, y = -x- cx³, 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). 3. Consider the nonlinear system of ODES: x = y, y = -x- cx³, 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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Sure Lets work through this problem together First lets find the fixed points of the system Setting x y and substituting into the second equation we g... View the full answer