Consider the Legendre DE: (1-x)y - 2xy' + 2y = 0 a. b. Indicate the corresponding...

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Consider the Legendre DE: (1-x)y" - 2xy' + 2y = 0 a. b. Indicate the corresponding Legendre polynomial solution y (x). Using the reduction formula, prove that the second solution Legendre DE on the interval (-1, 1) is the infinite series given by: x Y2 (x) = In (1+x) - - 1. (2 marks) satisfying the (6 marks) Consider the Legendre DE: (1-x)y" - 2xy' + 2y = 0 a. b. Indicate the corresponding Legendre polynomial solution y (x). Using the reduction formula, prove that the second solution Legendre DE on the interval (-1, 1) is the infinite series given by: x Y2 (x) = In (1+x) - - 1. (2 marks) satisfying the (6 marks)

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