Find the G.S. about x, = 0 for the following DE's 1. (x² + 4)y" + 2xy' – 12y = 0 (-1)*(k + 1)3a,x 2k 2k (2k – 3)(2k – 1) 5 Answer: y = a, + a,x +za;x³ + k=1 2. (1 + x²)y" + 10xy' + 20y = 0 (-1)*(2k +...

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Extracted text: Find the G.S. about x, = 0 for the following DE's 1. (x² + 4)y" + 2xy' – 12y = 0 (-1)*(k + 1)3a,x 2k 2k (2k – 3)(2k – 1) 5 Answer: y = a, + a,x +za;x³ + k=1 2. (1 + x²)y" + 10xy' + 20y = 0 (-1)*(2k + 1)(2k + 3)(k + 1)a,x²k - 3 (-1)*(k + 1)(k + 2)(2k + 3)a,x2k+1 Answer: y = a, + a,x + k=1 k=1 3. (x² + 4)y" + xy = x + 2 1 1- ao Answer: y = > anx" = a, + a,x +7x² + 2 - ao x5 + · 320 ... 24 48 n=0