Consider following simultaneous differential equation system:

y1(t) + 2y1(t) + 5y2(t) = 1

y2(t) + y1(t) + 4y2(t) = 2

(a.) Write down the system of equations in the matrix form.

(b.) Derive the characteristic roots using direct method.

(c.) Find the characteristic vectors.

(d.) Derive the steady-state.

(e.) Write down the complete solution.