Convert the second-order differential equationinto a first-order system in terms of x and...

Convert the second-order differential equation

into a first-order system in terms of x and v, where v = dx/dt.

(a) Determine the vector field associated with the first-order system.

(b) Find all equilibrium points.

(c) Use HPGSystemSolver to sketch the associated direction field.

(d) Use the direction field to make a rough sketch of the phase portrait of the system and confirm your answer using HPGSystemSolver.

(e) Briefly describe the behavior of the solutions.