Question

5. (15 Points) Find a series solution for the following differential equation. Calculate the radius of convergence. 2(x - 1)y' = 3y

Answer 1

= 2(x-1) 4' = .34 let y = frala Cotrips + C2 x ² +Cgoca a & Cnoch no y's Enchan una From O 2(xt) y 3y co =) N20 20x+) Ž En mensen _3 ² Chain E non am - 2 En nen xm- 3 3Cmapace =) 2x Enen an ni Иә Canno =) 2 { n cnach 2 {(ha) Choix" - 3 ni nas -) 2 nai nos untut nanoin. + Gacho) Cmn –3en') x? Witoin lupa lui) 2 § nendest + (-2C0+0) Cogn -360 +ELE-2) (90)69731 na CO = -20, -360 + { (2ncn - 2(6+1)(n+1-31m) un na an -267-36. + [c2n–3) cm Icn - 2 (not) Cmos ] xºc nel -2 (-24,360 20 (2n-3)(n-2 (nn) Chanzo

2 (nrl) (nr = 36 -2 -20 (2n-3) (n = EY (G= Co Chri fan-3) (2n+2) ch n=1,2,3 - y= Co to, & + C₂ 2c2 +6₂ x3 + cuk" + Cot 260 x + ( x²+ (2 X3+ Cuscyt nal C2= n=2 G (3 = = 6 no3 - 4 C +63)) (s = 26%) (32) Co (5 = 5 ca FC) (%)6 a = 76%)(3) (+)4](4) Cu = who ? nza lo 6 n=5 С. + y = to trix tez 2² + C₂ 23 tcux" +6, e5+Gx6 Cor 960*+ (2163** Ś C P ) coét Cu)(u)C)6 y = x4 +-

بی = پا ء ( 4 )( پ- x (4) 4۔ 3x -۱ (5-2) -- .3.2.7.ا (2) - ۱.۱۰ . 8.۔ 3.. W= 3 2. ما = ر . دا مجری۔ غدر - ۱۰] |+ 3x 호 1. 3, . (27 ) * 2 ) =3 د( .6.3 - (26) 2. = lim and an .. 3 .. 6.3.5 - ه -۲ - ( 2 + 2 - ) (242) be مه - د.3 .| (2-3) (2) دا .3 .6 ۱. 3.3 --- (2 - 3) دا .3 .6 2 ملا م و ( . 2 - 6 دهد (24) 1.3.3 – ( 2-2 ) .ل.13 - ) .. 2w (=v(ص) (محل ۔ 6.3. ۱۰ = (2017) (2-1) (27) 2wل.3 .| پر -+ (1-م) (1-2) (3) 3. 6.3. 2 27 مه در .3 . X )C۶۲) (274) ے .3 . 22 - lim لو۔ هد (2-4) C-3) (20) 2+ 2) beim Me (2-4m) (2-3) تمبر (2) ( 24 ) * - 1 1= ها (ک Q = 1 Rating of convergence |