AK-MATH225F10-WS7

AK-MATH225F10-WS7 - MATH225 Fall 2010 Worksheet 7(6.1 7.1...

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Unformatted text preview: / MATH225, Fall 2010 Worksheet 7 (6.1, 7.1) For full credit, you must show all work and box answers. 1. Using the power series method (centered at x = 0) on 23—y + 4y = 0, (a) find the recurrence relation. 7 : E Cm X0 ”7’ ‘2 "l C... X'1 r) =o W/Z.7 +H>¢ O zZoCax '+L;Zc.>< 0 18:! h: 0 m ~79 g 2 2w“ + 2mm” ' =0 "3 A>i W nvt - E— EZQCJ‘ + H Co»: X W O h:( 2” Cr) 'l/LZC-n—I :O - ? Javier», m, (b) Find the general solution. quite your solution In Signia notation. “w...w_.‘......,.l_.__.__ Name: \ Section: 30 lUlL/(ons (c) Find the radius of convergence of your series from part (b) 17m AAW m— n~§n 33/47,“ )LLW’XM' ’Pa’l.’ m] and n! ' \ :Zle)7“1(I-rn) (”04’ Mac” we “‘4‘ We :04} papa“ X JE ((1) Using a known Taylor Series, write your answer from part (b) 1n the form 1 (6 E ('Z)‘ )q 7 i o: o r) ' / ‘7: Co: ~Z.)< l y: f(m) (where f(:r) is not a series). 2 2. Using the power series method (centered at a: = 0) on Q + 4y — 0, dx2 _ (a) find the recurrence relation. 6Q _ W Znénvbcqx” 2“+ H 24,. >< = 0 n=2« ’750 :74 m $6 v Z “inflkn X + Z L! CVLXO a: 0 [3:2, V7:; Ain't) Cr) +‘an—a10 /{ Cf”: “COWIB / 0 9’2 (b) Find the general solution. Write your solution} in Slgma notat1onk 0:0 n”O,C,o A=l ‘» Cw Gina) . - 'HCa = CrLOLCc: “’9 ‘ C” was) Lt! . __.. C 35 ”3?.C77" :1)? ‘L'LU ' (c) Using known Taylor Series, write y6ur ansiaver from part (b) in the form N 7: fax“ / 7”“: ”CAN 2],:Zhb'llcn N n 3 7: ZCnx >c.+c,><+~c&x‘+c3><+ » ,... y = f (x) (where f (x) is not a series). x7 ; Cb Z l«t)”(z)z°><h + C, Z (4)” a)“ x’ZWfl (Lilia) n10 L20)l h=o (Zn‘f‘lll (29r/ 7: go 5 LL (My + a W L4)” (new <CZ)“/z>'* / firo (2-4): 2' ’1‘ {7: Co coda) +% 'S/‘qLZX)‘ 3. Using the power series method (centered at a:- —- )on (m2 +n1)y” + 2:1:y’ = 0m (a) find the recurrence relation. 71/13:? om) ”72 n C4 X’) L117 ’2an n‘bch X x 17U+7II+ZX7 :0 VT) , X2. ? n'Z r)" q '1': “Ca X4 (7"; 0 Zn [oldéflx +£né OCX 4'ng + ZO)Q,><’ #220, 3) le°3 :0 hZ. 7C2 + ((05:37? COX + Z [In at» Ska—14”?“ I>Cn+ZZn Z)Cna)/ y=o ZCL: o (/CB’fZ/é c3 C’FZ) (I) flaky/rm [n Dork 31%)an =7 ~¢ :LovflE—Cn—s) 43¢”, - (News): 8;? C3: 3" Co W - mtn-r ' ' ' p to degree 5 from part (b), find the solution guy to degree 5! such that 31(0) 2 0 and y’(0) = 1. ’=c,*C.xz+c,)€’+r~ 7‘ 3 '~' yzo>>co=o / 710) =a=$ 4. Using the definition of the Laplace transform, not the table, find the Laplace transform of (a) f (t) = 5 525% = 3;” flew : _ I; at)"Q 3— ° v ’ °° : ES.- CSt)6 “SAD : m 'C$+Z)t 30 25c it £1. 0” ) vL§+Lt : ~t I J | W 'k\* C [E133 FE “ (,982 6:12:91: 3 ~ I “(512)1': I D l ‘ (fit) C : 0-040 ~ W Ox , ’ (5+2): ...
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