Question

here is the question, and i hope that someone to help me out

Consider the following boundary value problem, x?y" + 15xy' + (49 + 2)y = 0, y1) = 0, yle/3) = 0 (a) Find the eigenvalues. (b) Find the eigenfunctions. Take the arbitrary constant (either cı or c2) from the general solution to be 1.

Answer 1

De Applying boundry Condor n²y" + inny't (49+d) y = Youco y (13 to you = G+ c three cases when 49-4d30 48t droit (M 44-2 5 (1) = Citch cita at C20 Cet 0 48+do x²4" + 15 nyl +(45+) y o ny" + isngl -o arry Cauthy Eulen method ci=0, C220 VO ergenchabction for Ast do (DCD-1) + Isoly. + 150] yo Aux. Egn m²m +15m so wolte memtly m=0,14 yos ge+ 8 142 Song - Sitemap

99714265 Pro 45+dzo = 4² I consagrad) logne tee Sin Jag toga Ny" + inyl + (49+0 y 30 Applyny Boundary concha الات (1) را x²911 of 15 rol of eeyo Uory Cauchy Gulan menanda [DCD + 5D & 42 ya (D+140 + 42 Jaro Aux &qh yret-0 You = 10 +6.0] To Set) - ceny se le ha generat Lees m²lum & 42 - ma 14 & 1142_4.42 tą Sim 14.9 m2 loges Test O+ (Sin I Sagu ma - 7+ 149 12 gets a ette a los 543 42 t et casin (45-led Cz Sin 49 42 7730 for non-aw ergen Juristes take a Sin 54942 = 0 i

UPRAR Pe Da 143 P T ny Case (3) 43t co = 4² 149-42 = 3n 49_ge = (3n) 2 45-4²= 5n2 4-1² = 9n2 2 yll isoly-iy a camny Eule methol (boi) + 15 D - 2] ge a To +150 - egye - 43-4 Aux Egh m² +140 - 1² = 0 ma-14 ± 5147442 da – an? be the edgenvalue and dna- gn? Sim s-an loga be the required ergenfunction - 7+ 49 +2 a ē ++ [14.5+ 427 (t) = -7-549+424 tege Sing = axt (7+ [Agot 42+ c 17-195744

Page L Applyny boundary cand yoooo y (1370 SCI) e G & GACA a=-a -7+ 4914 bels) = a(z) Trosts +49 tye 0 te (Ms 7 - Sassul G = Geo No ergenfunester