AK-MATH225F10-WS3

# AK-MATH225F10-WS3 - MATH225, Fall 2010 Name; or Worksheet 3...

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Unformatted text preview: MATH225, Fall 2010 Name; or Worksheet 3 (2.1, 2.2, 2.3) Section: 6:9! UJCIO/ls For full credit, you must show all work and box answers. 1. (a) Match the following differential equations to their direction ﬁelds. (All the direction ﬁelds are graphed for —3gtg3,—3syg3.) i. d_y_t (1) fil\$§=7¢éﬂ glop; Marks odor») chLTTZ-‘Al “4:3 Ach dt — ii. 53%:3/ __B____ Lil) £27; 5(0/¢\ Ark/L5 A104} [ﬂogged-ta] iii. d—y —ty & ll «65 «a. paralklv d25— (ZZZ/3%f/C'T) :O / Slopc, Mafkﬁ hofiéon‘ée\(7‘£ iv.@=(t—2)y ' 9:5 5:0 :3!” :CD dt Liv tag": ﬁdofc mwés Aefléontanf 7th 1 (B) bLZ/ .\\\\ \\\‘ \\ \\\‘ \ 1 \\‘\\\ \\\.\\ \\\~_.‘\~. \\\\~‘~«~. i\\\‘\\\ \\\\\\\’ \\\.\\\\ )\\\\\‘\ l“ V n , . I v%~/—.~4+—f~wi—4—-l-+%~+-\-~ "///ff «“///’/ "r’f/‘/,’/I ,////,//i ,v ‘\ \ \\\ \\\\ ‘\\\\\\ \\‘x\\'\\ \\\\\\ x \ i\\\.\\\.\ '«\‘\‘\\\\\ \\\ \\\\ \\'\\ \\‘\] \\\ \. \ .\\ \\\\\\\ \\\\\\\ (b) On graph (A), sketch an approximate solution curve passing through the point y(0) = 1. \$64 A hex/C. 2. The following differential equation maximum amount the environment can sustain. (a) Sketch the phase line (portrait) and classify all of the critical (equilibrium) points. E1 1 7’1 I, :O E? SJC‘L’C / [or ’\ H“f~¢.fd; of" ﬁlﬁk) , a 17. _-.—,» :B' onDL‘LblL ~7Z——""' Car fcpcllcf, or' 500'24.) A 4 0 7% l 754 at: I > O J t y?! 3% ( yrc LO . (b) Next to your phase line, sketch the graph of solutions satisfying the initial conditions: 31(0) = 2, 31(0) = -1, 31(0) = 5 74(1) = 11. (c) Find tlim y(t) for the solution satisf i t e inital condition y(0) = 2. —’00 TM E. '5 3. Given 3—: = ——1 + cos(y), (a) Sketch the phase line (portrait) and classify all of the critical (equilibrium) points for in g y Sjm F V '2’ ' 27137] 56m? strip/c ————~- \ +C657 r Lor‘ ﬂbvlé) 6°37 3- l Zo/j; . . Oz7/éém1-5EKLIL 7 (or— ’709’6) ,t : - “Z. 40 231% l 7 : *TT’ 240 ‘5 l7:37f (b) Next to your phase line, sketch the graph of solutions satisfying the initial conditions: 7r 4. Solve the following differential equations or initial-value problems by separation of variables. Put your solutions in explicit form. g, 2:... L‘ i : A‘é g 25X Jx / #0, 7:0 7: WWMWMWM 7 Cams tint 59/96:») z _x_. 5 +6 6, a 5 lyl =¢é s a. L a 7:1aes //}::¢/O 1» 2 (b)%;=x:t3x, x(0)=—2 Ax __. 1,2 t MW?) - L WM” 3 worrm=~2 5. Solve the following differential equations or initial-value problems using the Method of Integrating Factors. Put your solutions in explicit form. dy —5t (a)E—5y=3e —\$(: vlot g 1836/ Jf ‘51: V 3% +(~S)>’—5c ' _ _O 5.9% ~51~ 66%} = i C! t+C_ xult):6 > ’0 C 5% +695): 7 - 3:: 63 7 r ’0 C Ct: < ‘Slv >/ __ C:|Dt WW 6, 7 ' d 2t (mg—gteee t>c> _L’:Z_ t Lt 4’1 C. ox _ w L» at 3 ‘ C ’ 26 ‘1“ 7f, 1% :i- — Zia t .t / ‘ L-t at M” J? = 32260 alt _L_/i_ (JV t 7 if: + é’t 12\$ 1:636 (c) (x+1)% +y=1n(x), y(1)=10/ >90 0 \ jézb & _I\ :Q'ay )zxéax-erC 3:)? + 7”" y X-H yéx X-I—I S Walk Zn) xw) an am 0 “MC NCV)'—’6 :8 ;@ Ix+t 7L1): Z =10 X50 _ >42 . Q v>+c~a3 (Mi M +; -; ax Q>;) LLX+0j>I :QAX (KH) 7; 32" X‘JX URQWIX Agra” .. \s ._ (X‘il> 7:X’€AX—SJX AU'§JY§V"X ZX+137=><Zoxvx~rC ...
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## This note was uploaded on 02/08/2011 for the course MATH 225 taught by Professor Staff during the Fall '08 term at Mines.

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AK-MATH225F10-WS3 - MATH225, Fall 2010 Name; or Worksheet 3...

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