Question

b) 2(x+1)y' + y =0

Solve this DE using power series

Answer 1

Here I'm using power series solution answer is below any query comment and rate my answer thank you.

* some this DE using power series 6 2(2+1) y't y=0 solutiasa Given DE U 2(x40 y't yao let solutions of o.E anan n=0 ท-| y = E nam xon n putting in @, veget n-1 2(x +) { nana n=1 O + { and to n 2x Enam no no +2{ nana + anazo n20 121 DO n & znana + 2 ny nana no1 & anxoco ne! + ne0 n n1 a 120 no DO no & (2n+1) ann & 2 & nann & (2nHilan 2 " t 2 (ner and a 20 + C2041) an] acto comparing both side, we get mold 2004) ant & antl) an to noo 00 { [2 (111) and hoo

2 (na) anal =- (2 h 41 ans anal : (2nAllan a(n+1) in the recomance relations for no.1,2,. ho ata -(200) ao & ar -20 22041) ካ a2= -fou+1) a, -391 4 -3(-4) 390 20141) n=2 - a = -(2/2) +1) a2 212+1) 5a2 6 -sleutel 6 - 1500 48 n = 3 aya - (2(3)+1) a3 213 +1) 793 8 48 8 105 ao 384 an 80 om equation becomes co ana no a dota, at az 2² azn 2 3 105 ao nite y = ao+ (-26 x + 39 & x + (-15) at 48 2 3 aon+ y 1500 385 105ao 384 39 .» = 40 8 48 3 21+ 58 105 ge4 to--) =90(1- 2x + 33 - 384 3 2 is the Ex4.) B 105 x + 48 384 yo au 1-2x + 8 required power series solutions of equations ② where and is constant. Thank you