In Exercise 1, we consider the partially decoupled systemExercise 1.(a) Can you choose con...

In Exercise 1, we consider the partially decoupled system

Exercise 1.

(a) Can you choose constants in the general solution obtained in Exercise 2 that yield the function Y(t) = (e-t, 3e-t)?

(b) Suppose that the result of Exercise 2 was not immediately available. How could you tell that Y(t) = (e-t, 3e-t) is not a solution?

Exercise 2.

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