When N is a positive integer, the Legendre equation (1 x2)y 2xy + N(N + 1)y = 0, with 1
Chapter 1, Problem 26(choose chapter or problem)
When N is a positive integer, the Legendre equation (1 x2)y 2xy + N(N + 1)y = 0, with 1 < x < 1, has a solution that is a polynomial of degree N. Show by substitution into the differential equation that in the case N = 3 such a solution is y(x) = 1 2 x(5x2 3).
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