{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

finalrv2solns-2

# finalrv2solns-2 - M427K Differential Equations 58045 2nd...

This preview shows pages 1–10. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: M427K Differential Equations 58045 2nd Final Review Thursday 3rd May 2007 INSTRUCTIONS 0 You have 3 hours. 0 Calculators are not allowed. 0 There are 9 questions, each worth 10 points. 0 Write your solutions on the question sheets, in the spaces provided. Indicate your ﬁnal answers clearly by drawing a box around them. You must Show your working in order to get full marks. It is strongly recommended that you work out your solutions on scratch paper before writing on the question sheet. FOR INSTRUCTOR’S USE ONLY .1: .2: .3: .4: .5: .6: .7: .8: M427K Final Exam May 12th, 2006 Question 1 Find the solution of the initial value problem y’+ty=t7 y(O)=2- I.» I ' we“ ﬁrm? '9 jig/(k {is XH) -: e "- 6 M427K Final Exam May 12th, 2006 Question 2 [10 Points] Find the solution of the initial value problem dy_3x2—l d1}.— 4+2y’ explicitly. S06) (ma/4M6 W wllw M427K Final Exam May 12th, 2006 —-——-———————__—_____——_—__—_—_ Question 3 [10 Points] Find the general solution of the ordinary differential equation (3102.7; + 2mg + 3/3) dx + (x2 + yg) dy You do not need to ﬁnd the solution explicitly. AA {Aka/W‘va \$1041} JUL Do ~+ Wk 7, 2x S3 ,\ : €31 Mpg C. BDLLQ3X7 + szhkj l 7323ki>dlx + ()LIKSKA 7189967 :0 ‘1 Mme/ii w<117> ‘3: U’W’D‘l rs «x/l/w éol’vﬁba M EL 2 3* t 3 3,: 2 mleshrﬁc“ 50 LP : 127e Jr \$72 +C 1 Mlt D“? : glLe/l’ﬁ] {. Zoroaskl. 7363L+L|(X)‘ 53L \ M—i Ct(1):o cﬁ/L CLL So 44!: Mlﬁlﬁm ‘3 M427K Final Exam May 12th7 2006 Question 4 [10 Points] Consider the autonomous ordinary differential equation Where f(y) = 2(y —- 2)3(y + 1)2.(y + 3)- dy_ E—ﬂy) 1. [4 Points] Sketch f (y) vs y. S93 2. [4 Points] Find the equilibrium solutions and classify each according to its stability. r ‘ E: LLV‘N 64-0/3» sub“) 7 t: " 3 \7 : V l (,4le 1 * ' l 3. [2 Points] Sketch y(t) vs t. I r M427K Final Exam May 12th, 2006 ————_________________________ Question 5 [10 Points] 1. Find the general solution of the inhomogeneous second order ordinary differ- ential equation 3/” — 2y’ ~ 33/ = (—815 + 6)e"t. ., _. \ v‘ ‘ val-«bx 32/3 : Cmpz)(~+\>vo 4) M~~3J 3f: ’ —t_ 80 7L: g, 6 leve CM) 7', ; @131 gr) a“ w ’ 7’; ; (,AtLJFQR—{ék + @4216 . wt w“=<1\u + H—[email protected]>+r + WWW ' ma V [+ we e ~~ A + w —— 1 16+: 3r CY/A’uﬁ +i53> : C'Xtﬁq’ so: +8A>~WY\$= + ) lee-463E Zj')HA:<6,A-:1 1, + [3:2 ) :3) K:‘- 2. Find the complementary function and a suitable form for a particular solution of y" —— 23/ + 2y = at + at cos(t) + sin(t). You do not need to ﬁnd the undetermined coefﬁcients. M427K Final Exam May 12th, 2006 Question 6 [10 Points] Find the general solution of the ordinary differential equation xzy" + 5mg + 4y = 0 given that 311(av)=x_2 is a solution. i c: V be (‘M 7 t: V I :1 Al 7‘ZV' ’zu 7":V «LB'J‘ £3 /‘ w.— "—‘ 2 ‘1 )3 “’3 J 9&1 3; } M427K Final Exam May 12th, 2006 Question 7 [10 Points] Find the general solution of the ordinary differential equation y”+\$y’+2y=0 about the point x0 = 0 by using power series methods. You should ﬁnd the recurrence relation and formula for the general term if possible. c4 «Q 3-— —— A 1“) \r ;, “(L h“ 7 l :1 Z awhmm '|) 7w: L X441<m4ly M) A: J ‘ h: I “ti; Sks’bShV-vl’w‘hlzwo .\/\ C I: i“ 3%)“ (4% [BLAJAkLA + Ila/LA'I + Qééxnv :0. 4:1) +1, my, oil .2 l + Q «C, i 00 : g x + /\0\ “hack J , L L th (n+2) (,W‘Ll) 4 A: | A Mr: or L : - or.) “H mm “MW—M “ m N M/'/ a : r L 01A {gr 4 2 l 4+1 wﬁﬂﬂ Ow A A i l , a : Il’f a! b Q/ ZIL-l—i It; 7" ’l \ ' A. ‘1’“ M427K Final Exam May 12th, 2006 Question 8 [10 Points] Solve the initial value problem y” + 23/ + 22/ = 9(t), y(0) = 0, y’(0) = 0 where 5sin(t) 0<t<7r t: _ g() {0 ﬁg using the partial fractions expansion 5 _ 23+3 23—1 (52+1)(32+2s+2) _s2+25+2 s2+1 (l- MW .5gsl/Lt = 56;le T HWL+>SQFA Question 9 [10 marks] Consider the periodic function deﬁned by f(96)=Ilc for —1 S a: < 1, with f (x + 2) = f for all :1). Use the Euler—Fourier formulae to calculate the Fourier coefﬁcients of f. ...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern