Question

(1 point) The second order equation x2y" + xy + (x2 - y = 0 has a regular singular point at x = 0, and therefore has a series solution y(x) = Σ C+*+r N=0 The recurrence relation for the coefficients can be written in the form of C.-2, n = 2,3,.... Ch =( (The answer is a function of n and r.) The general solution can be written in the form of y(x) = Ayı (x) + Byz(x), where A and B are arbitrary constants and 91 (x) = x" + 2 arxtni, »2(x) = x” + b,x"+"? 11 < 12 n=1 n=1 r1 = and r2 = Find aj, a2, 03, 04, 05, 06 and b1,b2, 63, 64, 65, 66. Enter your answers as a comma separated list (21, 22, 23, 24, as, 96) =( (b1,b2, 53, 54, bs, bb) =(

Urgent!!!

Please show all the answers and clearly mark them and please show values of a1,a2,a3,a4,a5 and b1-b6.

Thank you!

Answer 1

- 5 crtner+n-Dox?xN+Y-3 we've 1 From the egy pedig"496x)}'+ R(x) y = 0 P(x) = x² , 8(90) = & R(X) = ? I we've already given that X.-o is a rregular singular point = So we can assume som in the form 103017 هن y = { marth ano ertnes ya NO of yn hirtnertry), 2+1-2 nao renal we've gºz? +x'+ (x *)=0 --- + (x ² ) x & Ertnntr-o entry & Crtmandant noo rtn n=o. ntr no no co intrt2 I nx 6f cm xertion nzo nco n+2 n ntr terenicna no =0 Cng & tn 69 n=2 nar -O Etemirtaucher-n) x+ 27 thy] + Garanth NGX-77446FC), or [ {ch 18th 12gco Jahtrt [ Chant s cof 723F3+9&c=+12-843 + Efen (6492.jpg)+c? Equating thocoefficient get 6/82 24)=0 n=2 no 9 n=2 on both side we 9 69 9 1-0 69

3 9 8 92 67 =0 - I CEO & On 9-688+)75-2;-12 671012) : % +0we obtain the indical equal the initial ean V2 =- For r = 318 (n-2 Cn 3 0 3 8 64 -CN-2 .. corresponding ho ni we've constant an - An-2 mln++) le in = 2, 3, an a to, 91=0 -90 Q2 = - 995= 0 SI aq 2 (2+) ? 19 = 0 +90 4 (4+3). 2(2+) 90 616+ );9(4+5)-2-(2+3) For Y 3:32. Corresponding to ry we've ao constant bn -bn-2 bn In(n-314) boto 161=0 ba 1b3=0 1 -60 3 9 by b4 - 212.319 (9-25/"b5 = 0 b6 : Final Solis an bo 212-8)914% (6-8) 64 (n-han (9-647-+)) 3. 290 (9119219394959)-[0,- 1990, 73019 2018iX 11/19 (babaituz, bai beszbo) = [0, -260,0 -2bo ... 2o.-4be Fil=h2 -400 ) -90 yon 5x13 5X13X 63
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