exam2 - Exam II I could not find my work solutions or a....

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

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

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

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

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5

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

View Full DocumentRight Arrow Icon
Background image of page 6
Background image of page 7
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Exam II I could not find my work solutions or a. blank exam, so this is a recreation of exam 1]. Enjoy. In. Find the general solution of the differential equation 1;” — 9y = sin L Lamagem ecu: JOIUHOnI \I —c(\l - 0 rqrtmulgy' goln ', VP: A—gin (:1- {3 (as t‘ 1?” l — \(P ‘E — ,0 {3(03 t 2?..n t 1). Which solutions stay bounded (that. is, y{!.) does not; go to infinity) as I. ~> 00? "Aqu hot/Q C‘ZO, 2. Solve the initial value problem 1.23:” — 2ng’ + 2;!) = 0, y(1) = 0, y’(1) = 2. Hint: This is an Euler’s equation. We. looK 4‘0" SOMS O4 g‘ovm \(3rt Flujary in $0 our ect‘laf'.Un-. 13 r- (r-\) €“~ 2+, NJ" +24J=o 50 £”( Mm) — 1’ +1): 0 So "(F~‘)*2r+1 ~c ~50 Fix-3,» +120 50 3. Find the general solution of the inhomogeneous equation y” + Gy' + 133} = 1. 0““ 9% F1+6rfi330 ‘ + F‘T—‘fi So F: Qu- 36 LLB 1 uélele Z 2 = *3 1 2i, 4a. Using the fact that yl = :L' solves the equation may" — :c(.’1:+ 2)y" -|- + 2)y = 0, find the general solution of the equation. We look {30/ a soim 04 “‘6 PW“ Y 1‘ X v I Tken \l'ng'a-V/ 7'=2V'+Xvu So X2(2v'1-XV" —x(x+2)(xv'rv) +(KF2)X V = O so xz(2v‘+x\,") - x‘(x+2)v‘=0 b. For which 11:0, yo, yf, does the initial value problem y(:l:o) = yog y’(:1:0) = y{, for the equation in (a) have a unique solution. )1 ‘L'fl l a): _. 'i 7‘ "0+ Cani": @ firo Un‘Twfi :Glm‘HOM £7 +‘ve axcsf-enfe onci umguemess 'i'keavww °"‘ “"7 Q8 x0960. So 5. l-‘ind the general solution of the equation y" — 21/ -|~ y = e' In 1. (Mint: The variation of 1 r 1 ( parameters formula is Y = —y./~‘fi}idt +312 #011...) 0W“ 91'“ 0=r“—2r+ I = (r—I)‘ 5" Y», = Cnet + citet Le!- : t ‘L 9/ \zetet W {\{i’jzg 2 :1" \fz ) — a . I, 8 (“get 6 Tku') t k t8 8 ln’t t 1"‘l 4: \ _.— *- .____H_\ a e. e w I— eat Cit + {:9 j e24; dg =—ef swat + tetflnedt dv U‘ V: du 6. Consider the initial value problem (1 — $2M" + 2y = 0, 31(0) = 2, y'(0) = 1. Write the first; five terms of the solution y(:v) as a. power series about 0. CO 6.: O0 .. n __ It _. - "'1 ._ \f ._ g QRX a) Y .— nZ‘: (1,. n (n 0X — [floann (nr2)(m-|)X \J SM“. Casr rum ferms W‘s/fl C), xiv" = E <2” n (n—I) xn “e” d° a “We 0‘- "of. So -0 a n 00 0: ('“X ) \/ +27 = 2 (0m (mummy -0n n (“t-I) +2an> “To 50 OU" r‘e Curran Ce he le- hbr’l 25 0r”: (n+l)(n+l) - an HUI-I) +2Qfl 2 0‘9—2 Q332—Il-o+1l=o =7 (lat—A3. On. H 3—-2.21+1.-2= => Iz'qqzo c3: =70“: 7. A small object of mass 1 kg is attached to a spring with spring constant k : 1 N / In. An external force fit) = £15th N is acting on the mass. At time t : 0, the mass is pulled 1m to the right from its equilibrium position and released. Ignoring friction, find the position function u(t) of the mass. m:i" t:( U" + U “3‘— (‘1 5m '5 Lilo): l, M'io):o r‘+ i=0 Uktctcost {—625.41 t U? 1; Atgos‘t ‘l‘ Bt 3;” t t; Timer wt) +s(2m-t-tsmon COS‘E', A:“2 tCestt sat ~24 2L1 U '1 ’1tcos“: P H o t U301 +U\P:C[cost+ Cgsmt QtCs h :M(O)=Qt _ $.12] a 2. -— 2 1 .4. asmt "Z‘ECOSt q Is», Li , ,_ M Ma + loud-- +116 +e/M rhea '1 5 \‘j/ final» as La <35) I M o sounds; mar». my? {m .i *9 a 1; q l1} udes ( Have We sow «VI ( ‘E‘ ) ...
View Full Document

Page1 / 7

exam2 - Exam II I could not find my work solutions or a....

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online