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q11a - m SEW QUIZZ 11 MATH 2233 SECTION 2 SPRING 2011...

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Unformatted text preview: m SEW QUIZZ 11 MATH 2233 SECTION 2, SPRING 2011 INSTRUCTOR: WEIPING LI Print Name and Student # SHOW WORK FOR CREDIT !!! SHOW WORK FOR CREDIT H! (1) (20pts) Seek power series solution of the differential equation yu+myl+2y=0, 500:0 (a) Find the recurrence relation; '7 H m - ' . J "1 5 V)‘ (W! M ' a 3 2 an X“ f gilt: MS (“T'Jﬂm-r X J g in; T2) )qu-aX i450 DQVG W 00 m (54 M . ‘ - ‘ z - (“+Z.)('"+') (twee x + X ﬁgmﬂ) lg”?! X I 2 kg) (3“ X 0 I110 ’90 - ’ 4 De ‘ i ‘ «Ff —- D an+2 4' X \$071,” 4141:] X ‘—" ; if,va I ( K I» H W“( 9:9 K .M “:i k ‘4K X 2 ‘l ' ' i A ' ‘ ' ' _ V, bu v QﬁZCfo + “Zlé’lrdaxzmﬂwfgq KW.” Z m a)" X 7 z; D WEIPING LI (b) Find the ﬁrst four nonzero terms of y and ﬁrst two nonzero terms of y1 and 1/2. , v.—Mﬂ_ .- .44 “1"Q0 “74 a“? h (h+z_)(mr‘l) \ _ M"“I n-._CiL a.___f_ii._.___.~40:ﬂg a;- 2 A 4:- 5 - 3;: 5 I ‘ > 2 _ '3' , 41. 5 7‘ g ifilao+6h7<+43x 4—; Z 3 ‘ “1; goK4+‘~¢ v 1- X9 .M ’ +"‘§;—j" +\\\> z, 9: , BFVX‘ +5“ *1“ v x3 ' 3 l 32;: K- ‘i’ \ (0) Evaluating the Wronski W(y1, y2)(0). - * / .41X3 ' /‘ ..._ 0 3 v:_. -.r..____ ’u»: k 33(0) ’ , y] X 3; T J 1/, (0) ya" 7" ( 0) 32(0) :0) WW 13(0) 5 i“ 2&1“ “i 2 730) Wm) 75(0) (d) Find the ﬁrst four nonzero terms of the initial value problem M yu+\$yl+29=0a y(0)=4, y'(0)=—1. _. r i. ’m' 33‘4éoanxy‘ 3/(o)=—4— l"; QOJ (o) " i 2 F 3 {L 6t. ...
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q11a - m SEW QUIZZ 11 MATH 2233 SECTION 2 SPRING 2011...

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