Question

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-3 incorrect -0.107142857142857 28 At least one of the answers above is NOT correct. (1 point) Find the indicated coefficients of the power series solution about x = 0 of the differential equation (x2 +4)y" xy +y= 0, y(0) = 4, y(0) = -7 y-4 7x+1/2 x 1/12 4 x -1/5 x80(x9) -3/28 Note: You can earn partial credit on this problem. Submit Answers Preview My Answers

Answer 1

"(x^2 + 4)y"" - xy' + y = 0: y(0) = -4, y'(0) = -7 let y = sigma^infinity_n = 0 a_n x^n be the session solution. Then y' = sigma^infinity_n = 1 n a_n x^n-1 y"" = sigma^infinity_n = 2 n(n - 1) a_n x^n - 2 so we have, (x^2 + 4) sigma^infinity_q n(n - 1)a_n x^n - 2 - x sigma^infinity_1 n a_n x^n - 1 + sigma^infinity_0 a_n x^n = 0 rightarrow sigma^infinity_q n(n - 1) a-n x^n + 4 sigma^infinity_q n(n - 1) a_n x^n - 2 - sigma^infinity_1 n a_n x^n + sigma^infinity_0 a_n x^n = 0 rightarrow sigma^infinity_q n(n-1) a_n x^n + 4 sigma^infinity_0 (n + 2)(n + 1) a_n + 2 x^n - sigma^infinity_1 n a_n x^n + sigma^infinity_0 a_n x^n = 0 rightarrow (8 a_2 + 24 a_3 x) - a_1x + (a-0 + a_1x) + sigma^infinity_q [(n(n - 1)-n + 1)a_n + 4(n + 1)(n + 2)a_n + 2]x^n = 0 "