Question

A power series solution about x = 0 of the differential equation y'-y=0 is Select the correct answer. YOU MUST SHOW WORK ON SCRATCH PAPER AND y=Σ * (2x)! +,Σ_o 28 +1 X (2λ + 1)! νεεΣ. *(2x) +σ,Σ. x (2k +1) γεςΣ. * (26) +0, Σ., και 28-1 (2-1): v=c,Σ. ΚΙ(2x) +σ,Σ. ** (2x-1) Ο γιο,Σ: * (2x) +c, Σ. x 28 (2+1)

A power series solution is about x=0 of the differential equation y"-y=0 is

Answer 1

Here I'm using power series method to find solution here first option is correct.solution is below any query comment and rate my answer thank you.

* Given differential equation is ylly=0 suppose y capen is a solution of equation & but DO (kxk CO E KW KA K-2 y"= { K (K-1) CK? K2 put all value in we get K DO { K (Kal) (k? 21 { cka=0 KED k muke power a S same for first sum for this put kokt2 È (k+l) (KHUIC, & Ckako kt2 kro op k E [(kH) (K42) 442-47 x ² = 0 comparing coefficent both side, we get (Kal) (K-2) CK+2 olk so (K +1 (K42) CK42 ilk Ск (K +12 (6+2) recuurrence relation kco, 1, 2, (6th = is the magnet

Co Mow 17 old Koo 2 21 ( 012) kol C1 3! 1 (2) (3) 6 (2 coles co2 (6 16 4 1 C45 214) (21) 13)(4) 3142 Gal k=3, С (3!)(1205) 을 5! (4) (5) (42.15) an so put this value in veget - k ka y = = 6+ (1+2 xt. to 4 Intan 2 lotut at 21 3 2 + + 241 3! 2 14 y = 1 1+ xt n... 2) 41 2k akt) y=6E q x is the required t power serier Kro (2k)! kso (2k-1)! solutions of Here from options first is correct Thank you