Consider the second-order linear differentia equation y" - y' - 2y = 0.
(a) Verify that y = e2t is a solution; then check that y = e-1 is a solution as well.
(b) Verify that y = Ae2t and y = e2t + e-1 are both solutions, where A is any real constant.
(c) Verify that for any constants A and B. a solution is y = Ae2t + Be-1.
(d) Determine values for A and B so that the solution of part (c) satisfies both y(0) = 2 and y'(0) = -5.