Question

Use the power series method to solve the given initial-value problem. (Format your final answer as an elementary furtction.) (x-1)y"- xy+ y = 0, y(0) =-4, y'(0) 5 3 + 12x2 y Need Help? Read It Talk to a Tutor

Answer 1

(x-Dy"-2y+y that yeZanx of given ali frerential Now IS the Let us assume Solution equetion n Cn-Da n-2 n:2 teshittiog よy 4 get n Now sub we 20 x-)Eno-Danx-2 ncn-) an x - EC + ne 2a2tao) t C2 ) Cntz

c the coeficient to Hho equatiog zeo ao a2 2 if C42) LHI) Oag -0 Cp tay ICHDar 2 a-6G3 = O 3 1 if 2 (at aa 6a3 2 (2+2) (2t1)a4a 12 a4 3O -ao S 1 aus 12 1 Go J 12 2 2.3 2 A0 24 ao 24

2 3] 41 since 3 + aocea) a42 Noco ao (e-o)+ a0--4 -4 ao CLo--4 -4 Ce- a45 Cy ST The required of the power senes solution egn is given oifferential 42+42 +52 -4e9