questions below:

Find a power series expansion about x = 0 for a general solution to the given differential equation. Your answer should include a general formula for the coefficients. 2" - x z' - xz = 0 . . . What is the power series solution to the differential equation? O A. z(x) = a0 1+ _ (-1)n .4....(3n-2)) 3n +3 x4 " (- n(2.5.8...(3n -1)) 3n+1 (3n)! (3n + 1)! n = 1 n = 1 O B. Z(X) = 20 1+ [ (-1n (3 .6 .9...(30)) 3n + a x + ) (-1)n(1.4:7...(3n-2)) ant1 (3n - 2)! (3n + 2)! .X n = 1 n = 1 (1 . 4 . 7 ...(3n -2))2 x 30 + 2 1 x + (2 . 5 . 8...(3n -1))2 O c. z(x) = a0 1+ 3n + 1 (3n)! (3n + 1)! n = 1 n = 1 O D. Z(X) = 20 1+ E (3 . 6 . 9...(3n)) 3n +2 x+ (1 .4 . 7...(3n - 2)) 3n + 1 (3n - 2)! E (3n + 2)! n = 1 n = 1