Find two power series solutions of the given differential equation about the ordinary point x = 0. Compare the series solutions with the solutions of the differential equation obtained using the method of Section 4.3. Try to explain any differences between the two forms of the solution. y'' − y' = 0 y1 = x and y2 = 1 + x + x2 2! + x3 3! + y1 = 1 + x2 2! + x4 4! + x6 6! + and y2 = x + x3 3! + x5 5! + x7 7! + y1 = 1 − x2 2! + x4 4! − x6 6! + and y2 = x − x3 3! + x5 5! − x7 7! + y1 = 1 + x and y2 = x2 2! + x3 3! + x4 4! + x5 5! + y1 = 1 and y2 = x + x2 2! + x3 3! + x4 4! + These solutions are recognized as . y1 = 1 + x and y2 = −1 − x + ex y1 = cosh(x) and y2 = sinh(x) y1 = x and y2 = ex y1 = cos(x) and y2 = sin(x) y1 = 1 and y2 = −1 + ex The general solution obtained from these two solutions is y(x) = ,