In Exercise 1, we consider the partially decoupled systemExercise 1.(a) Using the result o...

In Exercise 1, we consider the partially decoupled system

Exercise 1.

(a) Using the result of Exercise 2, determine the solution that satisfies the initial condition Y(0) = (x(0), y(0)) = (1, -1).

(b) Using HPGSystemSolver, plot the corresponding solution curve in the xy- phase plane and compare the result with the curve that you would have drawn directly from the direction field for the system.

(c) Using only the solution curve, sketch the x(t)- and y(t)-graphs.

(d) Compare your sketch with the x(t)- and y (t)-graphs of HPGSystemSolver.

Exercise 2

Use the method described in this section to derive the general solution to this system.