{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

apm255fa09exam1solutions

# apm255fa09exam1solutions - APMZSS Sept 29 [email protected] Exam 1...

This preview shows pages 1–4. 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 is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: APMZSS Sept. 29, 2009 @4091 Exam 1 Instructor: w. Zhang Instructions: Close books and notes. Show your work and justiﬁcations. Calculator for performing computation, integration table, and blank scratch paper are permitted. Student’s Name: Mark: 1. (12 pts.) Identify if the following ordinary differential equations (ODEs) to be (i) linear or noulinear, (ii) separable or non-separable, and (iii) autonomous or non- autonomous. . ‘ A‘gﬂxz _—.-. 2 41—2 ____ FL fZ/QWM 3'; it; xiii—«2o; Ebb/W7! WWW .—__ 1 (H?) P®)w’—(y-l)2=o :37 24/; 517 z. a- —— as 9' (1/ 2 ‘5‘7’3/7ﬁ/M/ééa {[2}? M/WMW5 2. (40 pts.) Solve THE general solution (i.e. all solutions) of the following ODEs. (a)xy'—2y+x‘=0 7? ﬂbécégzaz‘i 63f t (b)y'—2y(4—y)=0,__ ﬁll/h: ( __ iii? 2 J #7 ﬂ 973 ‘7’?) 27f g + fé—jy/g :M‘Z‘C .-~ "\$7 :5”: JMW"2§C¢W}:QZ+C :7 if” :‘QZ’IL‘C- ﬂ/aﬂz’rw 2:220 —-=> 5’26 51%. j/ﬁﬂﬁﬂm ?’ /:o?,Z’+C, 3. (18 pts.) Find the particular solution of the initial Value problem y’-2Iy2*3x2y2 =0, y(1)=0. ﬂ/ 2- ﬂ’:@z r32“)? ‘2’ :37 27% zéz 2-52”) 2 :fézz—t-jzjﬂf—g, .27 Fiﬁ-:1 +2 +C, 4. (15 pts.) Find all equilibrium solutions (ie. all critical points) of y' = y( y + 2)( y —3)2 and determine whether each equilibrium solution (critical point) is stable, unstable or semistable. &:g/=2(3+2)(g*3)2' :pg/aeg £223] £23 M X/ ,‘ (73475252! . r— H ““ M F‘— /7/% 797/5/‘4/1’1' f" / 5 igyii) 5‘ 0 0 a We) 2(4) main “2/ p 3 9; 3%) :«w (0270 5. (1 5 pts.) Suppose that at time 2' = 0 one person in a class of 43 people has heard a certain rumor. After 1 week the number 13(1) of those in the class who have heard the rumor has increased to PG) = 3. Assuming that P(r) satisﬁes a lo 'stic e nation when will exactly 22 people in the class have heard the rumor? When will all people in the class have heard the rumor? ﬂag/I Meéa/ ﬂag—3 3;;— s/em *7?) #275677) {fig/g %/m’f :7 wig/Frﬂfc #ﬂFF-VZ’I/ﬁhf-Fﬂgﬂ—X-C #ﬁﬂﬁ wﬂcrgzc jam {7(0):}. 2%: 76%; *—7 \$5425 'L/ﬂﬁjzk +é/ﬂe) .ﬂ. 7...}... . ’77 K 43%” 3'35?” =§j¢ﬂg 25.99, agééS” - %/é’// ﬂaw? jug -—.,/»7.24= Z: ﬂea: 7.; #2. ﬁg- 7&4?» M H ﬁg; “ Jig? : o/zw,éi ﬁzsz/yggé) %%47 f”? “3/ ...
View Full Document

{[ snackBarMessage ]}

### Page1 / 4

apm255fa09exam1solutions - APMZSS Sept 29 [email protected] Exam 1...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online