Question 9 A function f(x) satisfies (1 – ~?)f"(x) – xf'(x) + f(x) = 0. = (a) If n is a positive integer, what is the va

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Question 9 A Function F X Satisfies 1 F X Xf X F X 0 A If N Is A Positive Integer What Is The Va 1 (72.97 KiB) Viewed 32 times

Question 9 A function f(x) satisfies (1 – ~?)f"(x) – xf'(x) + f(x) = 0. = (a) If n is a positive integer, what is the value of K in the following (6 marks (1 – x)f(n+2)(x) – x(2n +1) f(n+1)(x) + K f(n)(x) = 0. n n Hint: (f9) (n) (2) п = Σ(1) f(k) (x) · g(n-1) (), where == k n! k! (n-k! k k=0 = (b) Given that f(0) = 1 and f'(0) = 0 find the values of f"(0), f(3)(O), f(4)(O) and f(5)(0) Hence, determine the Maclaurin series of f(x) as far as the terms in x. (4 marks)