Question 9 A function f(x) satisfies (1 - 2%)S"(x) - xf'(x) + f(c) = 0. (6 marks) (a) If n is a positive integer, what i

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Question 9 A Function F X Satisfies 1 2 S X Xf X F C 0 6 Marks A If N Is A Positive Integer What I 1 (37.12 KiB) Viewed 35 times

Question 9 A function f(x) satisfies (1 - 2%)S"(x) - xf'(x) + f(c) = 0. (6 marks) (a) If n is a positive integer, what is the value of K in the following (1 - ??)f(n+2)() - (2n + 1)/(n+1)(x) + Kf(")(x) = 0. n Hit: fax (a)=() (2) - (a), where © g) n! k!(n-1)! ko (b) Given that f(0) = 1 and f'(0) = 0 find the values of S"(0), 3) (0) (0) and f(0) Hence, determine the Maclaurin series of f(x) as far as the terms in 4 (4 marks)