M293F08sol_eigen - Math 2980 Worksheet: Eigenvalues and...

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Unformatted text preview: Math 2980 Worksheet: Eigenvalues and Power Series Solutions 1. Find all eigenvalues and associated eigenfunctions for the endpoint problem M y/I + Ay = 0; yQ—Z) = (Ly/(2) : 0- \ ,f/ A’fl/ My 4wéx)-Hffl%£¢jjfl’/’ “Mflflhé/ZNMIEK/{g [Val/pfl 5» fl: MWfl'ZKjV‘gm/éz") 9%: KIWI (29‘ y/f/z) w w a s: .704 we? Au} 4 xflw 62%) 2- W m (Exp KM 4%! ~~——— ~~~~ _..~. W WW; / mam/w 6&2 ' M WMDZQ @VI/mfl fiwjflmm " 52 fl: {WW/Mw)vW/w) /~~ " . :r/ Mr WK, Mm 4+6; 0 .91» MQA)'*{§I’1’I){JM}969 ‘ A“ ‘ :m RA ': 1 W ?_M__.@); 5/77 Qly A) 6—K“ g; /:/‘14 fold}: “5&2 92:1 5 77' {7! 2r “a ‘mw 7) W) 43'” 94) {at/mags); f/ iJazzzqiumzrnifrct m4 H 1 4’ 5"“:"v "H‘Wf'i A "£5.77: “ aqufzg (#15537 #759)L72 WA}? ) Z /éVJ x9 n. v gig/16w} wwfifr/ I)“ 6% we. M.,_—/ M/ MTFfiW—es‘saution and radius of convergence form—the differential equa— - "W tion ‘ (-76 —2)y’+y = 0- M\ g“? M ,1,» K " K? I Ln~l 9g fly” flfmz ?1 ’4‘": “in; W '3( Do . I .— _ I1 *7?— WWE” : §n4¢fl"ggzncm”' 4*,544” r g: 64775”: ééiirflfigéwc/ “a M w n. M x - 3mm 52am, 2" + 2&1 [ Mm 95W?) 1 54 r260 . 14:0 14:2) . 4, “Z a gym/mi 326111)ch w r, 0 yr. 1: " ' [4-50 ‘ _ S a % / fi 99 W M g} J35: (/1+//(6h yum/9 a”, = &‘“/,fl, 3. Use power series to find two linearly independent solutions to the differential equation y”+9y = 0. . 04 M b M W (é: Zfl/fli’ddfizflaszrzé‘lfl (’9 I V J , A, M fl"! . fly} ‘ M ’1 / V x o)— ”; : ggfyflfdgflhgfifl‘éflg I I(~_; % 4&vflaqfill" " ":5 V I a y first] = gflhde/Jawh) ,Z’L * fl 1422) ’ W W &/ 5W ' w w‘ J) C * m/m ” (WM 2 l H '27 h ,L , a {4/ King. Mflé _ (er Ma, 6 , (7) //2w// " Wol 12w ” W “M W. haven h M Maya/14 2"” w Va ; [gt/W; 5” 9: 7L [214W ’7; amfl’llz “2”” 1" IL abd/ neg” 75] +14 ’4? filial ...
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M293F08sol_eigen - Math 2980 Worksheet: Eigenvalues and...

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