Proceed as in this example to find a solution of the given initial-value problemy'' + y = sec²(x), y(0) = 1, y'(0) = -1
a) First, use the differential equation y'' - y = sec²(x) to find the general solution of the homogeneous equation y'' - y = 0.
b) Then, use the method of undetermined coefficients to find a particular solution of the nonhomogeneous equation y'' - y = sec²(x).
c) Combine the general solution of the homogeneous equation with the particular solution of the nonhomogeneous equation to obtain the general solution of the given initial-value problem.
d) Finally, use the initial conditions y(0) = 1 and y'(0) = -1 to determine the specific solution of the initial-value problem.