HW1Key - Due: Assignment #1 At the START of tutorial on May...

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Unformatted text preview: Due: Assignment #1 At the START of tutorial on May 18, 2011. No late assignments will be accepted. 1. Find values of m so that the function y 2 arm is a solution of the differential equation m2y” + ny’ — 6y 2 0 for all m > 0. . (a) Verify that the ODE d2y dy w + 3a; has the 2-parameter family of solutions +23; 2 e—z (b) Find the values of c1 and 02 for the initial conditions y(0) = 1 and y’(0) = 0 . Consider the first-order ODE (1) (a) Show that y(:1:) = 0x2 satisfies (b) Use the Theorem of Existence and Uniqueness to justify the solutions of this ODE for initial value y(:c0) 2 yo. . Find the critical points and draw phase portrait of the autonomous first order ODE ill _ dx _ Clasify each point as asymptotically stable, unstable, or semi—stable. By hand7 sketch typical solution curves in the regions in the my plane determined by the graphs of the equilibrium solutions. eytyz — 2y)- . Solve the following initial value problems (a) 3323/ = — x2 + y2 — (mg/)2 with y(1) = 0 (b) (1 + mag—g + 2mg 2 Where with the initial condition y(0) = 0. $2; ,1,“ fl —1 -7\ I Btu):_(l'1-Cl)e .& ‘+(2)(7~CZ3€’ ’k . , “7-K s .9, <~L+x~tci)~\ 4C1}: fl ’ "K ‘k “a + 3‘6 ‘f LVX s L 31-“ (MN) SJ” -2. ~7¥ ,,\ _‘ ‘ C C 3 1—1 'C e 2;) :Q (-Zfl“? ‘ 1' a ‘? L __ ) .,_ «fix "'1 'l J g C + 11 a f 4‘ 1 Cl \ y) {L “fl? (a, {‘er M /C\o.\ 4/ S "Lt/(Ll \ 6 Par{ [0 3(0)? ‘\ f3 0 -§ C‘ 5r C2 = i ' *- l C = n M) 3%“ O ‘3 1 (he) 2. U CI-f CL :- \ «=3 [1—— Cl )~ CL 17—) ,0“ h’fo <0 Q1- 1C1: C- cl; a & ). FW’ 0* ) H / \QLM) _ ’_ -6 e (i-‘L I.) -cha 1C6, ZK a) g C N “(/an x __«_ - 9. “a S 0/“ 3 2. \blele— ,_,3 le‘Cx)" 1C7” 5 i“. (4/ WM we» WH‘) (Rm Cuwslm‘fm «Ci 41¢ 151;»; a» alum/L r Cgvfoaykfiflb alvk LjLL'ft-bw/fi Ck (/jtfi 0'4}, 50 ’ f” ’ I—TT' O (/Kmftk [JPLU , I a, , w; 7/1144 J 136 v V/06 170.3,- Zfln Q, (3-) ) I I F? an lktasJ/J) '3 / 3 v! 2) f 0 fl 3141,, J/ [Law] a)‘$¢,-£ ’fi . 5° |‘A\(‘J 0A Cc/W cup/Al; 0M ‘ “A ' am/ '1; @me :3“) ‘7 . C - p ‘ ‘fénbé. 6 HM Coat) MW 1“? :3 1m : (\-m> (H32) _______..1 : L____L _.\ l-f m 1, #3 L (Cafu-v\\25 : - _. w .t C L ( - 33. , —— ’1 FL '5 (L f r . / L I ) < l T ) K 5;) 0V1 ‘ we, a J Jw mta 3 WV -3”. _ ‘ ’— : 4 /)L ‘V 7‘ 1 C < /L If: ux. ‘(j - fl 5‘ at C. ' er~ /7, < A ~e V‘ L Q /L “(d4- C (Mp/(,5) ” 4 "/*7\~BC “an “yrs /2 "' 3 < Q at (3ND C r “0.1 7 ‘ S j (:69, mule/1‘1 36- C - (5 L ’ L5 C - n... 1/; : q~-‘ ,'Lfi‘11 0/ ‘9 L/-" L. k M‘V‘Cx l“ L“) , 0 ¥ 3 (“ii—‘1’" $wi: \ & w; \* La -1\ 9L >‘ a}; F) {Lg “(B‘ka Elma/{‘- ‘3‘ 3 1* JW ‘~x(\‘t%z) [41—1 L z e; ;’ ve/ : \‘l’ 1v ‘ 7x (H13) 0 k < \ Z)\ \‘f'hL (l4fi‘ ” l -‘L (HT:) “A >/ |1NL L __ r . . C 1x... g‘ r ‘ l w/L “E C,‘ O \ \6 (1": 7‘ ) :— L .‘7 -— 0 At C‘ *3 Ci 0 (\Avwh/ 172 (/“(MV “3! ‘Ww‘fm’g’ L?“ 0 47k 4\ \1‘}? L SLA\(‘/‘ CW“. ’ .~\ VA d z , 1.),\ a 7L _L..—a K'fP/Z) iii..— \+I;VL \‘V'FL : - LL. '9 Lu?) X.s\ WA" ’M‘L S l L“ s "' " V r a 02’ ('1' =5 flm ’9K S 1‘ X1 1“, \— 1—:1 ’k—djl -i I , _ L)) ,Q.~,~ wk = _L( 4) + C.7,/L-— “’5 b3 ‘H 1% .l-r 1" .L, 2- F.’ ——————-—-’x 0 Q ‘\ 4‘ 11(‘1' 1L.) 9—“) " s “A L ‘ ,1. + 2. 1x. 2 ____,_______._.==ss 2_ (1* Li) ,L/ a éqk 4 \ ,/ (\4’7‘})1 «0 1?: V‘ mz‘ L ‘1’ ( 14>?” ‘ r f "f : ( [A/Lui/flx £3 Yl’i (,thmawb J 79‘ 5-1 (1L. OM {JACK/[Io I {3y Ck Sa' \— 4 a Ca cf "(0 A {L} 1343., \?vr\(; t I :Lffvp. E Mammy b chm" X} “’39) 0Lch Eu 1% a? i ...
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This note was uploaded on 01/15/2012 for the course MATH 201 taught by Professor Steacy during the Fall '10 term at University of Victoria.

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HW1Key - Due: Assignment #1 At the START of tutorial on May...

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