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

Convert the second-order differential equation

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

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

(b) Sketch enough vectors in the vector field to get a sense of its geometric structure. (You should do this part of the exercise without the use of technology.)

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

(d) 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.