Question

(1 point) Find the solution of xy" + 5xy' + (4 + 1x)y = 0, x > 0 of the form Yi = x n=0 where co = 1. Enter r = -2 Cn = - n= 1,2,3,...

Answer 1

Qolution- consider the differential equation spy" + 52. y' + (uta) y - 0 xo Note that isa regulas singular point LCH Us consider the Golution of above differential equation is, as jollow s. 8 +0 2 Ľ anan. differentiate w.7.4 x, we get 8th ya an no 89-1 ya į (srn) an 8+n-2 y". 18+n) 1870-1) an x no Substitute these values in equation "" 846-2 oo 2 16+7)(8+0-1) and 58 8+)-1 E 18tn, and no 8AM + Cuara) e ana o btn E lsan i (8540-1) ante + {5 (810) ana no 00 co %+n 8++) E yana f E an 12 TO

--) -т ((49) (~4 - ) 5 (+n) + ч аn ҡ h ох toate - ana т. б +N) 3 (s+n) (*+n+ч) 4mx 3- Y . - E a noi го n20 8 (+4) 4ч4, * * з ((sm) (+ + M+4) + ч1 ч. am m2) ЛЕЯ р -+ ҳ 1-4, 3 У (s(8+4) + ч чох* + 3 {fw17) Кst m +ч ) + чJ 4* *n-i3 @e K4T.о с comparing both sides like Power of x. ( s($t 4) +ч) q, а р a - (n+s) п + ч%+ ч (2 +s) - •2. -2.. 22.

[(dan) (santu) + u] an - ant GO: [ht (htuted cured] (isu) when 1.-2. 47 : ani h+(aru) (3-4) an-1 hth-zu ani นรก : (24) 2 when Qo: +1 An . Cap. ana (nen n? thank you, plz sate.