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) «@4 (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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Differential Equations Test 4F007 - NAME 5 problems 20...

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