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let-f-x-1-x-2-1-find-a-d-e-wich-verify-f-x-2-prove-that-x-R-n-N-1-x-2-f-n-2-x-2n-1-x-f-n-1-x-n-2-1-f-n-x-0-3-prove-that-f-2n-1-0-0-n-N-

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Question Number 30747 by abdo imad last updated on 25/Feb/18
let f(x)=(√(1+x^2 )) 1)find a d.e.wich verify f(x) 2) prove that ∀x∈R ,∀n∈N (1+x^2 )f^((n+2)) (x)+(2n+1)x f^((n+1)) (x) +(n^2 −1)f^((n)) (x)=0 3) prove that f^((2n+1)) (0)=0 ∀n∈ N
letf(x)=1+x21)findad.e.wichverifyf(x)2)provethat∀x∈R,∀n∈N(1+x2)f(n+2)(x)+(2n+1)xf(n+1)(x)+(n2−1)f(n)(x)=03)provethatf(2n+1)(0)=0∀n∈N

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