{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

M232summer08_test1_solns

# M232summer08_test1_solns - FquOX class Problems w-‘il...

This preview shows pages 1–6. 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 is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: FquOX class: Problems w-‘il we?“ be 9+ 4144's [‘5 90 0 c9 ‘ Mae W5 I ’7 Test I Off-H 4 I MA232 Summer 2008 P W‘hm - Differential Equations [You must show work to receive full credit} 1. Classify the following differential equations: (10 pts) (a) The Mathieu equation for a vibrating pendulum: 2 935% + 27% + w3(1 + t):c=0. 2"" «Aer (lavendemr an‘dble 1‘5 x indepew den-1' \lcwx‘able 1‘5 i‘ 0355 LFV‘Ca( Variable (oev‘ﬁrrm’f homogeneou5 (b) The Fisher—Kolmogorov Equation (found in combustion and crystallization problems) 2 Qa—:=u(1 — u) + 3—53. 2'“, orécf aerJen-l VOWNble ,‘5 LL Mega/«Jan Van‘mbl€5 are, 31 and f PDE Non lmemr nanlfnear fevm f5 UL.(I"‘*) 2, Verify that y is (or is not) a solution to the differential equation. (note: only 1 of the 3 is not) (10 pts) (a) t+yy’=0, t2+y2:1. \IZ: l‘tz 79W 1- t2 -l 7' =1; ~2t) (Pt?) /Z ‘12 ’I’ i + (m?) (thi’ it) V45 2 "0 (b) y”'=et, y=et+at2+bt+a F \g'> 65+ Zat + L \ ‘I "3 6’5" Z a > jut: at 1/15 m (c) y’+y=t2—2, y=Cet+t2—2t. \VE cet+zt»z I} 15 Ce &ﬂ~z+ (c 4 52%: = 52,2 Xho 3. Verify that y is a solution to the differs the initial condition. (10 pts) ntial equation and determine the value of C which satisﬁes (a) t3 + yew/=0, t“ + 314:0 (y > 0), y(0)=1- a. bad: m +0 Check 7Q( + 0‘" ‘/ v= (c— t“) “ (b) ty’=3y,[\ y=0t3, y(—4)=16 KKK: 5(£2 z 3 Wow I~C— /_ 1‘ Ci = at 3 a "L 3 )/ ‘62::(44) —7 6’ H . S m \\\\\\\\\:////II/II: . 1|] 4 ‘ s % \\\\\\\\\._///IIIIII , \\\\\\\\\._////IIIII e w _ I. r ‘tittziiiié “MHZ”: ZZZ”, r. .\\\\\\\\\..///IIIIII VIII/Ilz’.— ’xllllll u \\\\\\\\\.—////I//II42 III/III’._ a 2 W \\\\\\\\\://///IIII III/11:: ’ Z: \\\\\\\\\_r///IIIIII I —lIIII///—_ I 2 .__— .mw \\\\\\\\\—_////IIIII ltlIII//’_ / _—.. a \\\\\\\\\..///IIIIII .lllIlIl/a_ I . ..__ tam \\\\\\\\\_./xlllllll llllllllz_ I '——— d \\\\\\\\\..////IIIII AIIIIIIIIII, I a a’f’ \\\\\\\\\.—///IIIIII 4 V. lllllll‘\~ .\ 1”; w \\\\\\\\\~—/IIIIIIII II.||.|I.\\\— \ 1/ I S|I\.\\\\\ 4 I d \\\\\\\\\——////IIIII 2 . \ . d \\\\\\\\~..z//IIIIII. “ \\\ \ l on \| \\\ \x..///IIIIII._... \\\\\\\~._ ~ 4 \\\\\\\~'r///IIIII |\\\\\\~.. \ m ﬁ\\\\\\\\\“.///llllll \\\\\\\-_ x d . \\\\\\\\\ .IIIIIIIII4 \\ \\\\~.. ~ 1 \ t rl Til. . C » a .. . a 4 4.. «Iii \\\\\\\~.. ~ ._ 6 pm A u a .. p 0 L4 ¢ 6 t c B e r. r. O C e h t h t .m n m s I I’ h 9 . 0 Lu Jl h 0 2 _1 7? C, “HM: arrec‘n‘an I / y :“y 4. Match the differential equat (10 pts) y/ / 3/ =9; 8) M 6N‘ec‘h‘on grab 6(Wés OW i éfpewdS J w PT n. d F ‘T c e C V IO M A 369mb on ‘5 WM 5. Solve the initial value problems by separation of variables. (15 pts each) (a) ty’ — 11:0, y(2)=2. 6 ~ 0‘ Ir C - f at ’ ‘l [K 2>cm ~> 0’ \ ‘ , ______ 3‘4""‘ t” (b) gal—ﬂ, y(1)=—2. Pcoblem ti )7 Wk homewoFK 437/ on “WK pay 6 \ PM 0% class: Probkems \ aca ,‘n \[adr nai‘es. (c) y'=ty3(1 + W1”, y(0)=1. “(z ,_\_ ‘ 1 v %ctﬁg(l*tz) 117- ‘ W‘Z“ ’ l 2-: .— ‘ \I 1 [0“ t‘)'z-§ cl ’ \ ‘ gﬁhkty M: _,/Z 117’ “Ft-“Ll 1;:%_Z[0+t23/2+C13 ‘9": T; :6,“ a) I- . t 1‘6“? 31 (p1 C 4/1 I: Ii’Z(H()B z'zam) a (,2 ‘72 "° iéﬂiww nm ® 0(6? pd+ 7A 3-(‘ J16; ‘3 fwuemulq m “~ng ‘ answe( (d) 312%? 9(2)=0 531 u T U“ ‘ ’— “ Z (375 I111 Kt: ‘ [Winn-‘1) ‘14”1 z I» ‘f _ sfv’li JHL‘RQ‘A 611/2 0: '*W) i 2— Z he, CD WONG ...
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