ODE test 1 2017.pdf - Ordinary Differential Equations Test...

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Unformatted text preview: Ordinary Differential Equations - Test 1 ,—~ @ February 9, 2017 NO ELECTRONIC DEVICES. JUSTIFY YOUR ANSWERS AND SHOW ALL YOUR WORK. Name: ® 1- (20 pts.) Solve the differential equation. Give the general solution in explicit form. gy—Gcoswcs— 1)+y'=0 linear 7’ r g; 7; awn/q) (fa-Lt": ,2 6535*: [email protected] I ea": 3: cosx’(1+3y2 00393)y =0’ y(0)= (Safefi‘ffw a? u-nZ-ues fa]: £5111)! ( Cosx— ' 1+3)! 605 5,7»: 7/5? > 7 "ya C 4:25;: 41/ 1 f6?“ : g“ (“XJJK j + 3y16673)a/y a“; 505% [\fc' } \_ ‘fiv ) 3yszJyJ _ th - _— ja5(¢)J‘: 5,8[9 6 +‘(, : y H5903) 3y} m cat: , - 0’ 37" w Page 2 f" 3. (2-5 pm.) Find the explicit gmwral solution of: 2 iii“ 2) y: = E + T e—(y/xr‘ :1: / 83/2 ‘5‘éfi [In I (and? 7’- _L _ x1 —()’/x) j. r/ ‘ 3—” a a 44" X 7 7: 362.9 ax+w / ‘ 535 ”3-) Find the general sulntion of: E #61" 1/ (21312 + e”) + (2z2y + ey)y’ = 0 5' (25 D‘S-rgr‘rlvrs’ihe diflorvntial equation. Give tho solution in oxplivit form. , 2 y — :ij + 4313/2 = 0 K“ Irma/[,3 é “EL-3— ~ 3/2 x f 7 ‘- ~97 y; 7'31 , .4. ‘ (L ’ 4-0.: 7— a/u};.l_ “24 2 AL, _ “:4; .32.,J— - g,’ "341324.: 40 X 49") 9% dx a, . “244/ 2 L/ L'nflr x a” 7’ “‘i x /- L; J”,\ / \ /” (’7‘): -\ X 'v-T x ~2_ cl fl :' X-I _. 1 R A £749 ‘— / “I L '2‘; X X j,..7¢j_;‘/_1’ 2‘ J» ‘"‘> 5», x1”: ~L/["-'--) 47$ 50"} wk y: I; X ’69 l -—-— _ Lf .L. ,1 x7’“" — 7. “" 2;.1— ‘x‘Af A YVL X / O 6. «r ‘ 2:) pts.) Solve the following (liifvrontial equation. 2C” + (2(‘y + 3(2""’)y’ = (3 V K 1 z _ y 3 2 7 ‘9 In“; *(”’6' + In 4) <3: '(2:7+3"‘)é_2:. , e, ‘ :0 L 7— .3 >’ 4' (y ’x )Jz w cl): " a Y1 : _'_ 1 ' d)‘ 7&7 +X3cly >2? K— ' z \ )(‘k( _ 3 Infcfir‘ in __ , 7 ’fJJ), :0 ’ ’ raw“ 4,: - ' 47 z .27 ’ L“ ~ 2 .- clx ‘— ‘3x -3X2——27 56311 77 a _./—; 7’ ' $72 2. y; e 7 )l : 6 hwy—2), \\\ \ \ \\ 77 I \\ \ Page 6 é...— ». r 5 11‘ - Dry" ”’4"! = U (m + ay )' -' 7;,irx an? fflgfw _E:_’L : 25-79 518.; ‘5. 9 .7 4x 7 lob) _ f): — Q), cl — N )( _ on Q ‘ :: 2§y7+3y7 % 7 __ :1 _.._.——;__Tl:. :2. g 3'": em»?! ”I K : —— X ‘x -—L f xszzx 24%ng =0 ( r (X *v—«fijclx ~ 977' JP ‘*‘ z. 29 " < 54’; .. .. ‘l , 47 :‘L dx — “E2; E9 , ' *4* we , “7*? x :. _ -/ y " x *' 6‘2: y -———9 Pony) : Inkl—xfir’v—jéyj ”9 C:/r,/)(I—x§$;g I 6,; 5"}? L3 6' z .. fx 3;"? 113(7) ’Exflicfl’ Farm 7 ' fin back - —- 7 .1. Page-7 L 51/); $5355»? : Q ...
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