(a) Solve (2) of Section 7.6 using the first method outlined in the Remarks (page 345)—that is, express (2) of Section 7.6 as a first-order system of four linear equations. Use a CAS or linear algebra software as an aid in finding eigenvalues and eigenvectors of a 4 ×  4 matrix. Then apply the initial conditions to your general solution to obtain (4) of Section 7.6.

(b) Solve (2) of Section 7.6 using the second method outlined in the Remarks—that is, express (2) of Section 7.6 as a second-order system of two linear equations. Assume solutions of the form X = V sin vt and X = V cos vt. Find the eigenvalues and eigenvectors of a 2 × 2 matrix. As in part (a), obtain (4) of Section 7.6.