Differential Equations Test 4F007

Differential Equations Test 4F007 - NAME 5 problems- 20...

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Unformatted text preview: NAME 5 problems- 20 points each 1 MAT 227 Differential Equations Test 4F Show all work for full credit! 2 if 0 S t < 27r Suppose f (t) = t if 27: _<_ t < 37r . Use the definition to find the Laplace sin 2t if t 2 37: transform.(You may use the table of integrals from your book, be sure to reference any formula used by the formula number.) Use the Laplace transform and partial fractions (show all steps) to solve the differential equation with initial conditions: y"+2y'+5y = 65 y(0) = 2,y'(0) = 3 Use Laplace transforms to solve the initial value problem. y"+x + 6y 2 O x"+x + 6y 2 O 36(0) = W» = 1 x'(0) = y'(0) = 0 Use the Translation (Shifting) Theorem (Theorem 1 in section 4.3) to find the Laplace transform of f (t') = sinh(kt) sin(kt) . (Recall: sinh(kt) = (61“ — e‘k’ ) / 2 ). Also, show your answer is algebraically 2kzs e uivalent toF s =——. q () s4+4k4 Use the Differential of Transforms Theorem (Theorem 2 in section 4.4) to find the s+2_s—5) s — 4 s + 6 inverse Laplace transform of F (s) = ln[ S24"? -—Slfl ’26 g '53“ -531? 5‘ W?" 52+? : (5 y :04) 33 W a. “42 ’ w [7] {7]45i5] X €55":ch if/fifflfl-W) an. A -56 é s¢ J6 yfl’yIZD) 42$ 50 f A (Mm) 40“ £5— e's I ._ W’Swfi' LS [Ti/(o) S c> {a 5 c; 5 , h\_ I V 55 ’1 9 + 9be 2 5 jfy1’25-§+é'5j[y]-é 16%], _:5 ' 5 Z Sf[g]4255f£'9] +5113] “35 ,3? 'jé £57} (92"25 +3“) - 25 _ =7 = 435* I '7 Aés'z+2>ks)4135‘+¢s W I ‘ C ’- u *5 Lffy] (€2%Zg+r§>\§;/'_§ +25 +9\ 3 S 5 > (“I LS .r {/3 r - ‘Z:fi 4'5 7 : 2 __ {rm 6? t 2% + C 5(52&25%S) ’ 5 €537.95 {ST'SA ls‘k‘ls wéS : A Earls ‘6)? @91ch ,[3 ; A B: is r ' 95?: A. «15 IS 4;- , ¢ /, ¢ ‘ ’ '7;- ‘r fig *7 g 4’” ,_ /5 ‘3 gm?” + [35 /1__ 2 ' v ' ,,,, _ WW 5 +0190? [3 H)” g W 5 ~23 L; W my!) 3) WW 1%?” X”+IY+6; 3 0 I"; " m? #9?“ L 95 A 55> 1£H«fi£w3—SW*%M ' I/ y m; y x» if: xfl'i'k’ié‘" X{f[;77/+J:L/><]4 4%]:0fig/ifr‘Z-Z/4f :9] =2; DJ ozgzgm -5» mg my} 5 f J3sz (§z%7> ' Iffl‘ifyj: g, 5 “+7 + 451% { W) “HQ 1» shah dyhé} 1’: Mi Fifi) 5”” 552"» am‘wewé 4‘“) £6le fifi>:«fi<£3fl3~a’ifism[m> -ng/ Va ‘1. 'L- f/L \\ ’ ZLSIK) +5 (54,92346‘ \ “A ‘ . Ix /‘ ‘ _ “MWWMV“W I “WA-x fl] fl/VL’“ I 2 “WWW” 5142444262“ 2 K2$ (L “hm-m" _WL, 1 54+ M4 5 9‘ salshnK“ gwazémm '1 WM}? +miiml> (6" 3 ‘HS (33"1514"?L W MLS +‘l ) 5 M496 L ‘l : L 2 55 '63 HZs'WH) use. fig, t 5:4 has A; c “ If ’61: mm. .2 5) F57 2% (mm 9""! 5+5 '2: Jr? ’gZ/BS’l? 52*23’2"! ’ / F5) [email protected] (52"33 4r?) “'gi/ézqfilfi ,2?) FZ>> :14 Q; a) ($63] —— %[é%’>[wée73 fglfj¢f”’ ] 2 ¢ 25+}— figr'gs’IQ “ 52 4,25 .2?! _._25%2- { _, FarJ‘mJ [radiant ! ,1 ’ /mrzj [afi #wm z; flaw) (Mam j WWW Zirfi -21L4 ; 5‘ fil~ +“l"/2$+2 % B ‘ WV. “’45” 2 I; :/’””~/’ (5423096) 5’2 6+5 (5+) (5 S)"’ém3 "7 “6"” 2 54‘). : Ag; 4) .1 gait) 233A+B 234+3 ’3 Z (in 4'25 23‘ é,” 78> '33:?! BSACI fl “if “I 4”” “Av” -L-s ) '6 Ci: $+2 5“ 3 % S’Q _l,. 62%;; ...
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This note was uploaded on 08/22/2011 for the course MATH 267 taught by Professor Willson during the Summer '08 term at Iowa State.

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Differential Equations Test 4F007 - NAME 5 problems- 20...

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