How would I solve y\'+xy=0 in matlab using the power series method Solution Assu

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Assume that y = S(n = 0 to 8) a(n) x^n. Substituting this into the DE yields S(n = 2 to 8) n(n-1)a(n) x^(n-2) + x * S(n = 0 to 8) a(n) x^n = 0 ==> S(n = 2 to 8) n(n-1)a(n) x^(n-2) + S(n = 0 to 8) a(n) x^(n+1) = 0 Re-index the sums: S(n = 0 to 8) (n+2)(n+1)a(n+2) x^n + S(n = 1 to 8) a(n-1) x^n = 0 ==> [2 a(2) + S(n = 1 to 8) (n+2)(n+1)a(n+2) x^n] + S(n = 1 to 8) a(n-1) x^n = 0 ==> 2 a(2) + S(n = 1 to 8) [(n+2)(n+1)a(n+2) + a(n-1)] x^n = 0 Equating like entries (with a(0), a(1) arbitrary): a(2) = 0 For n = 1, 2, ... (n+2)(n+1)a(n+2) + a(n-1) = 0 ==> a(n+2) = - a(n-1)/[(n+2)(n+1)]. n = 1 ==> a(3) = -a(0)/6 = 0 Hence, y = a(0) + a(1)x + a(2) x^2 + a(3) x^3 + ... ..............= a(0) + a(1)x + 0x^2 + (1/6) a(0) x^3 + ... solve remaining

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