Question

Solve the differential equation below using series methods. y” – 2xy' – y = 0, y(0) = 3, y'(0) = - – 8 Find the first few terms of the solution y(x) = 2 azxk k=0 ao Preview ai Preview a2 Preview a3 Preview 24 Preview 25 Preview Points possible: 1 License

Answer 1

Given differential Equation i's y"_22.7-y=0 46%) = 3 axe xH =_y'(X) = kaka K=1 K-2 y Σ KA K(k-1) ak put in 0 we get _K-2 Iakok =0 Z K(k-1) axx -] ak ak Kel F(x+2)(k+) akiz? 2 2 Kapak & akak_o kal Kro kal 222-9. + E_[(k+2)(1+1) akte - (2x+1) ax] * = 0 comparing coefficjent of both side we get 2 - 9=0 2 CK+2)(k +1) Okt2 (2k+l)ax = 0 (2x+) OK fk+2) 4k+1) akt2 = 3 since 7(4) = 40 + 4,7 + agat y(0) = 3 and y'(o) = -8 + 10 = 3 9,5-8 from 923 -az 그 39. -6 kufrom @ - (K-2) from ③ a. 2 -4 au S.92 12 11 blo

tk=3) from G -7 as 7 az 20 5 Answer ao = 3 a = 8 "( 1 ) Az 3 2 az = 4 au yo as -I s