(a) Find one more nonzero term for each of the solutions y₁(x) and y₂(x) in Example 8.

(b) Find a series solution y(x) of the initial-value problem y'' + (cos x)y = 0, y(0) = 1, y'(0) = 1.

(c) Use a CAS to graph the partial sums S_N (x) for the solution y(x) in part (b). Use N = 2, 3, 4, 5, 6, 7.

(d) Compare the graphs obtained in part (c) with the curve obtained using a numerical solver for the initial-value problem in part (b).